1 QUANTITATIVE RISK MANAGEMENT AT ABN AMRO Jan Sijbrand January 14th, 2000.
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Transcript of 1 QUANTITATIVE RISK MANAGEMENT AT ABN AMRO Jan Sijbrand January 14th, 2000.
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QUANTITATIVE RISK MANAGEMENTAT ABN AMRO
Jan SijbrandJanuary 14th , 2000
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Quantitative methods in banking
I. Risk and Capital Reserves
II. Modelling Financial Instruments
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I. Risk and Capital Reserves
A bank (like any company) aims to earn money inreturn for taking risk.
But:Taking risk may result occasionally in
experiencinglosses. In the extreme, banks may default.Bank default will have large impact on economy:
Depositors lose their money Firms lack source of financing for investments
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Therefore:Bank is required by Central Bank to hold Capital.Level of required capital is set so as to make
bankdefault extremely unlikely.
Sources of bank capital: Equity capital Reserves Subordinated loans
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Required capital ABN AMRO(1998, millions EURO)
Credit risk - on balance 13.474
Credit risk - off balance 3.137
Market risk 651
Actual capital 22.612
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What is Market risk?
The possibility to gain or lose on an exposure to market prices
Profit may result from– bid/offer spreads– commissions and fees– trading profits (?)
The banks’ own Capital protects against losses.The profit should provide a return on this capital.
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The value at Risk concept
1) Register current risk position accurately
2) Calculate the effect of market price movements (profit/loss) from one day to the next during the last thousand days
3) Present all these daily results in a histogram
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The Value at Risk distribution:Market Risk
1%
VatR
0
* Expected result (average): zero* With 99% certainty no greater loss than VatR* Bid/Ask spread etc. have to compensate for taking this risk
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What is Credit risk?
“Potential drop in the value of an asset because a
debtor may not fulfill its obligations”
Asset DebtorLoan CustomerBond IssuerDerivative transaction Counterparty
with positive MtM
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Credit Losses (1)
S&P Rated Corporate Bond Defaults (Mil. $)
0
5000
10000
15000
20000
25000
1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997
Source: S&P Ratings Performance 1997
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Credit Losses (2)
Probability distribution of credit losses
Average
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Distribution of Credit Losses
Non-symmetric (skewed)
– Large probability of small losses– Small probability of large losses
Long, fat tail
Non-normal distribution
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Credit Losses =
Unexpectedcredit losses
Expected credit losses +
Amount one expects to lose Deviation from expected credit losses
“Cost of doing business” Not risk, because expected
Unanticipated losses risk Capital as protection
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Loss distribution
Probability distribution of credit losses
Expected Loss
Unexpected Loss
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Risk/Reward for Credit exposures:
Reward comes in the form of interest margin
(interest on loan minus funding rate)
This income needs to cover– the Expected Losses fully;– a Return on the Economic Capital (say 20%)
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Economic capital
Capital needed to sustain potential credit losses with probability (=confidence level)
Can be calculated for: portfolio of assets incremental assets line of business
Also called Value-at-Risk (VatR)
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Portfolio models for Credit risk
Determine: Expected credit losses Probability distribution of credit losses
potential unexpected credit losses
Examples:CreditMetrics, KVM, CreditPortfolioView, CreditRisk+
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Main ingredients of Portfolio Models
Probability of default (credit quality) of debtors
Estimated exposure at default for assets
Loss rate given default for assets
Extent of diversification / concentration of portfolio (default correlation's)
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One-Year default probabilities per rating
0%
5%
10%
15%
20%
AAA AA A BBB BB B CCC
Source: S&P
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Exposure at default
Forecast of amount owed at time of default
Different from current exposure Forecast depends on asset type:
– loan facility: nominal amount, or estimated outstanding for committed but (partly)
undrawn line
– derivative: estimated positive market value
– bond: nominal amount
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Loss rate given default
Percentage of exposure at default which one expects
to lose
Depends on
seniority of claim on debtor type, quality and quantity of collateral
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Historic bond recovery
Seniority Average
Senior secured 58.52
Senior unsecured 49.60
Subordinated 35.30
Total 43.77
Source: S&P “Ratings Performance 1997”. Data from 1981 - 1997. Recovery as % of par.
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Default correlation
Likelihood of simultaneous defaults of multipleobligors
Depends on e.g.:
geographic diversification diversification over industry sectors state of the economy
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Estimating correlations
Bond credit spreads
Equity returns
Industry andcountry factors
Factor models(CreditMetrics, KMV)
Defaultcorrelations
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Loss Distribution +Economic capital
Probability distribution of credit losses
Expected loss
Economic capital
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Conclusion on Credit risk and capital
Modelling credit risk on a portfolio basis
presents many challenging modelling questions:
- Estimating default probabilities
- Estimating default correlations
- Assessing effect of economic cycles
- Optimization of risk/return
Results may substantially change approach towards
taking and managing credit risk in banking industry.
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II. Financial Instruments: Model risk
Mismatch: model and reality
Interesting questions:– How severe is model risk for
pricing/hedging of derivatives, market risk evaluation of a portfolio (VaR), etc?
– For example: Do we need to model a stochastic interest rate for a convertible?
Need for quantification of model risk!
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Managing Model risk
Models for derivatives are developed by commercial line in the dealing room (“frontoffice”)
Independent validation by Risk Management
One of the tests: Hedge Performance Measurement
Model reserve where necessary
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Hedge performance measurement
Derivative: Hedge instruments: Hedge ratios: Consider the hedged portfolio:
Uncertainty tomorrow hedge errors:
dtS )(dt )(
)()'()()( tSttftM
)(tf
)()'()()1()'()1()1( tSttfetSttftHE r
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Hedge performance measurement
Different hedge strategies (choice of and ) different hedge errors.
Different models (predict ) different hedge errors.
Estimate density of hedge errors (risk profile).
S )1(),1( tStf
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Application Dollar/Yen
Model: Black-Scholes (for FX) Hedge strategy: Black-Scholes delta
hedge Model risk profile vs. empirical risk
profile Test criteria of interest (e.g. VaR or
variance). Could interpret test-statistic as first
quantification of model risk
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Application Dollar/Yen
-.7 -.6 -.5 -.4 -.3 -.2 -.1 0 .1 .2 .3 .4 .5 .6 .7
10
20
30
40
50Density
Model based risk profile
-.7 -.6 -.5 -.4 -.3 -.2 -.1 0 .1 .2 .3 .4 .5 .6 .7
10
20
Density
Empirical risk profile
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Model reserves
Uncertainty in hedge error (up to 99%)
may be covered by a VaR-style capital
reserve.
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Summary
The impact of quantitative methods on bank risk
management
Market risk:Capital Adequacy Reserve based on Historical Simulation.
Credit risk: Modelling reserves likely to be Monte-Carlo based. Correlations stilldifficult to estimate.
Model risk: Ad hoc and sometimes quite complex.