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Economic capital models : Buildingblocks, strenghts and weaknessesFebraban International Congress of riskSao Paulo - October 20th, 2011
Vincent Sapin
The views expressed in this presentation are those of the authors anddo not necessarily represent those of the NBB
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Presentation
Overview
Context
General principles
Risk types (Credit, ALM, Trading, Operational,Funding, Business, Pension, Project, Reputation,Strategic, Liquidity)
Aggregation and disaggregation
Model risk
Stress-testing
Available Financial Resources
Comparison with insurance models
Conclusions
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Context
This presentation gives a summary of the main
choices that have to be made in order to obtaina useful estimation of the economic capital
needs
With focus on quantitative aspects
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General Principles
Risk identification
preliminary and crucial step
issues: exhaustiveness (cf. infra)
consistency within a Group
Purpose(s) of the model(s) clearly stated beforehand (e.g. reporting, monitoring,
solvency), e.g. : Point-in-time : quickly adaptative for risk monitoring; consistency
between risk measurement and price of hedging
Through-the-Cycle : more stable for solvency
Bottom-of-the-cycle : sufficient capital during a downturn
development / modeling in function of those goals
in practice, not always the case and/or not formalized
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General Principles
Central development of models improve consistencyand efficiency, but :
applicability of central models to local entities? quid if material activity/exposure at the local level but not
significant at the group level
granularity (e.g. equity indices)
Similar risks of the parent company and of the
daughters (or of different business lines) should beadded up in an integrated way (positions on same risk
factors are added up) or VaR aggregation with crude correlation estimates ?
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General Principles
Choice of a risk measure for Ecap :
Generally VaR (Fair Value based) = the maximum
potential loss calculated over a certain time horizonwith a certain confidence level
Loss = decrease in value
Over a certain time horizon
E.g. 1 day, 10 days, 1 year
With a certain confidence level
E.g. 99%, 99.97%
Expected Shortfall (tail-VaR), scenario analysis orstress-tests ?
use of the current level of risks, of a historical
average or limit level ?6
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General Principles
Time horizon :
default value :1 year sometimes lowered thanks to 'Management actions' - see
later
Generally immediate shock on the risk factors
corresponding to 1 year (freeze of positions): simple but incomplete picture
Confidence Level (CL), e.g. VaR 99.97%
generally linked to external rating how to interpret deviations between targeted and observed rating ?
transformation of CL sometimes needed (e.g. trading)
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General Principles
Calibration (see purpose of the model)
Point-in-Time vs Through-the-Cycle ... vs Stressed e.g. : use of historical data collected during a smooth period will
probably not deliver a 99.97 confidence interval
How to assess potential regime switch vs temporary event(impact on the future values of parameters, e.g. spreads) ?
Potential significant impact
Real-world for risk measurement (Risk-neutral for valuation) :
implementation issues: e.g. availability of parameters
consistency issues :e.g. based on different historical
series (length or time period)
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General Principles
Management actions:
Examples :
Trading and ALM : shock on a lower horizon than 1 year Credit exposure management (lowers exposure at
default)
Strong justification needed to avoid riskunderestimation (credible stop loss limits, evidencefrom the past, ...), and sometimes lacking
Keep in mind that they must be valid in the chosen high
confidence interval e.g. : are stop-loss limits realistic during a market crash ?
Only based on the past
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General Principles
Estimates should be forward-looking
Going-concern (or liquidation) ?
if going-concern : Is the remaining capital after alarge loss sufficient to continue activities ?
Buffer for usual variation in activities
Buffer for cyclical effects (especially with PIT
measures)
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Credit Risk
Risk types to be covered:
default, migration and spread risks (as Ecap is Fairvalue based)
Models (default and migration) usually based on Merton's theory (e.g
CreditMetrics) with a number of factors (e.g. :
sector/country/size) Importance of
granularity of inputs (e.g. transition matrices,
spread curves) the calibration: cf. general principles
the risk types covered, in particular for some
portfolios (e.g. sovereign)11
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Credit Risk
Advantages :
only one figure summarizing the entire credit risk ofdifferent portfolios
sensitive to concentration/correlation in theportfolio
stability of the methodologies
Issues with this type of models: numerous strong assumptions (e.g. Normal
distribution of asset returns, no tail dependencies)
calibration: time period used ('normalcircumstances) ?
Non-modeled risks (e.g. Spread) sufficiency of level of add-ons for non-modeled parts
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Credit Risk
Issues with this type of models (cond) :
Profit generally not modeled (non exhaustive cash
flows projection) are these profits integrated in AFR (through expected
profits) ?
approximations for some products
retail (e.g. mapping to an equity index?)
structured products (e.g. waterfall structure, transitionmatrices...)
high confidence interval (how to backtest ?) Intraday credit risk coming from settlement
activities
=> importance of stress testing/scenario analysis13
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ALM
Requires an Economic Scenario Generator, to
simulate all material risk factors (IR, FX, EQ,
RE, volatility risk ...) in an (ideally) integratedway
Full revaluation per risk factor (non linearities)
Implicit options (mortgage, sight deposits,
saving accounts, ...) must be taken into
account
Requires a risk measure based on Fair value
changes (ernings approach creates
aggregation challenges)
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ALM
Issues :
Degrees of freedom in interest rates dynamic principal component; 1-factor interest rate models;
Volatility and correlation estimation : choice ofhistorical period
Short term - e.g. 1 month - historical volatility
scaled with square root of time
Implied volatility risk missing
Normality hypothesis of risk factors
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ALM
Issues (cond) :
Linearity of products revaluation
Loss aggregation :
Var-Covar based method (silo - no integration) withcorrelations estimated from the underlying risk factors
(hybrid method) Simple dependency models (no tail dependence)
Management actions - sometimes used - butdifficult to prove
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Trading Risk
Based on well known VaR framework used for internalmanagement or regulatory purposes
Transformations to respect ECAP general principles,e.g.
holding period : 1 or 10 days => 1 year
Confidence intervaI: 99% => 99.97%
Sometimes management actions/stop loss included,considering possible hedging or liquidation of trading
operations
Sometimes based on the VaR limit instead of current(average) VaR
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Trading Risk
Issues management actions: enforceable? at what cost?
human action?
holding period and confidence interval of Ecap farfrom daily management
assumptions for the scaling, e.g. independence,
Normal distribution illiquidity in the market, e.g. bid-ask spread
volatility
intra-day positions
default/credit migration/spread risks
coverage of model risks : from pricers to VaR ?
length of historical period
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Operational risk
Two approaches, in function of Pillar 1 choice :
internal model (AMA) or not (BIA / TSA)
AMA banks : recalibration of the 99.9 % VaR(higher quantile, but also sometimes with more
severe extreme scenarios)
Non-AMA banks : use of crude estimates
BIA / TSA with changes (other historic period, floorfor low income activities, higher quantile)
First attempt of scenarios - based on RSA -sometimes used for benchmarking
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Operational risk
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Operational risk
Advantages of internal models :
improvement in the management of operational
risk: risk committee
loss data base
first quantifications
much better cartography of operational risks (entity andbusiness level)
=> virtuous circle (higher awareness)
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Operational risk
Issues for AMA banks:
large uncertainty on the results
Low frequency / High impact events difficult to
estimate and sometimes considered by banks asimpossible
modeling techniques still evolving and under
discussions (LDA or scenario ?) rescaling of the quantile with flawed hypothesis
(log-Normal distribution)
Additional issues for non - AMA banks : Insufficient risk sensitiveness of some simplistic
methods based on the past => increase ofscenarios quality
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Funding cost risk
Risk that the refinancing cost of the company
increases
New in Ecap models
Generally based on scenario analysis
evolution of funding requirements (balance-sheet
items)
shock on funding cost
Numerous assumptions, e.g. costs, volumes,
funding sources...
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Funding cost risk
Issues:
Type of instrument used (short or long term):
definition of the scenario, e.g. idiosyncratic, systemic... Importance of recourse to ECB, FED ...
(remaining) availability of financing on the market
Impact on new production pricing
Choice of the shock on spread (historical vs expert...)
Volume :
liquidity needs in the trading room (margin calls) difficultto anticipate
interactions between different variables / second roundeffect (e.g. behavioural)
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Business risk
Less advanced than operational risk
But should also be capitalized
Two types of approaches :
historical volatility
based on historical P&L series
cleaning : ex-ante (P&L) or ex-post (VaR)
volatility around an average (historical or budgeted)
Consultants benchmark
Sometimes use of scenarios to benchmarkresults
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Business risk
Issues:
Short historical series
definitional problems : border with others risks not always clear, e.g. ALM and
strategic risks : E.g. Commercial margin risk Business or ALM risks ?
exhaustive trash ?
Limited risk sensitiveness => try to identifyexplanatory variables
no use test => pure capital add-on
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Pension and project risks
Pension risks :
Potentially important (defined benefits)
Common risk factors with market risk (integratedmeasurement ?)
Project risks : Investments for an important project are made, but the
project fails
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Not (yet) capitalized risks
All material risks to be covered by capital
Exceptions to be justified with a validreasoning in case of stressed events
Reputation risk :
Often not capitalized as theoretically covered inother risk type (operational, liquidity ... risks)
But incorporation of reputational losses in other
risk module still to be proven ...
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Not (yet) capitalized risks
Strategic risk:
Often not capitalized
Possibly covered in Business risk ?
Liquidity risk:
'Bank run' risk Capital not the first line of defense
Often not capitalized until now
Planned new acquisition:
included in capital planning ?
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Aggregation
Inter-risk aggregation: market, credit,
operational ...
Integrated models vs Silo-type models Silo approach (Var - CovarVar) :
division of risks according to the company's
activities: credit, market, operational, equity ...
set up of a correlation matrix based:
on expert opinions
on external publications on proxies for risks under consideration (e.g. based on
historical data)
on a mix of the three
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Aggregation
Advantages of silo approach
single risk measure for the sum of risks and also
per risk type simple to implement
computation time
transparent (measure per risk type) Issues
applicability to local entities (distinction Group vs
Local correlations ?) tail dependencies
importance of calibration (cf. slide on general principles)
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Aggregation
Issues (cont'd) silo approach :
How to estimate inter-risk loss correlations (representativeness ofproxies) ?
link to confidence interval:
Isn't the Normal distribution used for the sum of the risks, when it's notthe case at individual risk level ? quid fat tails ?
average or stressed correlations (correlation increase in case of
stress)? under estimation of VaR ?
How to separate credit and market risks of structured products ?
second round effects, contagion (=> scenario?)
==> evolution towards an integrated approach (integrated simulationof all risk factors)
reliability of such estimates/ model risk =>implementation of add-ons ?
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Disaggregation
Allocation methods:
limited theoretical basis
proportionally to local entities (no incentive to locallydiversify)
change in the confidence interval at local level(compared to Group level)
Benefits of diversification (within a cross-border Group)
related to the transferability/solidarity assumption
this assumption should be proven/tested the retained method should be in line with it
concentration at local level should be taken into account
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Model Risk
In addition to the usual mitigation measures(statistical testing, independent validation,
stress-testing, use test, ...) :
Economic capital must be calculated for theresidual model risks (to cover for the un-avoideduncertainties)
Issues : clarification of the link with prudence margin in
lower level parameters
granularity in the application to foster continuousmodel improvement
better justification of the capital buffer =>
standardization of the process
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Stress Testing
Usually developed at the end of the process
Complement to the Ecap model => challenge
of assumptions and benchmarking of Ecapresults
Stressed VaR vs stressed loss (working
outside of the Ecap model !)
Historic and forward-looking scenarios +
reverse stress-tests
How to integrate stress test results in Ecap
estimation ?
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Stress Testing
Issues Still work in progress
Macro-economic environment difficult to forecast
and to translate into specific assumptions for inputparameters of specific models
Severity of the scenario (what is an adequate
stress scenario according to banks andsupervisors ? Has it to be realistic ?)
Generic economic scenario vs specific to thecompany concerned (e.g. business model)
Global stress-test still in development
Excuse not to improve the models ?
Consistency of hypotheses in retained scenarios
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Available Financial Resources
Input to assess economic solvency and to define riskappetite
Generally based in a 1st step on the current regulatory definition of
capital
then modified to take into account specificities of the
economic capital approach=> consistency AFR vs ECAP to be checked as different
environments at stake
Reverse approach more suitable
prior definition of criteria for inclusion in AFR (i.e.permanence, loss absorption, availability)
better integration with the ECAP framework
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Available Financial Resources
Examples of issues :
Transferability of own funds within a Group Estimated net earnings
Unrealized capital gains / losses
Coverage of EL by provision (consistency Ecap -AFR)
Intangible assets
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Conclusions
Modeling of 'traditional' risks more mature
Still a work in progress, given the huge methodological
challenges and data and IT issues Advantages :
Generalization of risk identification and measurement to allrisks (also less 'traditional')
Additional relevant - coherent and standardized - informationfor (Risk) Management (higher risk sensitiveness)
All risks summarized in one number
More resources devoted to Risk Management function
More objective measures, facilitating risk / return analysis, ...
Improvement of data quality
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Conclusions
Issues:
use of simplified models with constant parameters
(e.g. correlations) Silo approach
Willingness to correct simplistic assumptions that
leads to capital underestimation
Final Ecap number results from a multitude ofmodels feeding each others (from pricers to inter-risk correlation) : are models errors vanishing or
magnifying ?
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Conclusions
Issues:
importance of modeling limitation / choice
awareness and communication (e.g. assumptions,justification of calibration choices...)
with a high confidence level, crisis must be in thepossible scenarios and not only in the stress
testing large uncertainty in the results due to the high
confidence level and time horizon
Difficulties to perform conclusive backtests importance of different risks measures, i.e. models
complemented with benchmarks, stress tests,nominal limits ...
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O f f hi i
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Out of scope of this presentation
Pillar 1 models
Data and process Documentation
Internal validation of models
Model management framework
Governance
Use test
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