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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

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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.