QUANTITATIVE RISK MANAGEMENT
AT ABN AMRO
Jan Sijbrand
January 14th , 2000
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Quantitative methods in banking
I.
Risk and Capital Reserves
II.
Modelling Financial Instruments
2
I. Risk and Capital Reserves
A bank (like any company) aims to earn money in
return for taking risk.
But:
Taking risk may result occasionally in experiencing
losses. 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 bank
default extremely unlikely.
Sources of bank capital:
 Equity capital
 Reserves
 Subordinated loans
4
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
Loan
Bond
Derivative transaction
with positive MtM
Debtor
Customer
Issuer
Counterparty
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Credit Losses (1)
S&P Rated Corporate Bond Defaults (Mil. $)
25000
20000
15000
10000
5000
0
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 =
Expected
credit losses
Unexpected
credit losses
+
Amount one expects to lose
Deviation from
expected credit losses
 “Cost
of doing business”
Not risk, because expected



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Unanticipated losses  risk
Capital as protection
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
20%
15%
10%
5%
0%
AAA
Source: S&P
AA
A
BBB
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BB
B
CCC
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 multiple
obligors
Depends on e.g.:
 geographic
diversification
 diversification over industry sectors
 state of the economy
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Estimating correlations
Equity returns
Default
correlations
Bond
credit spreads
Factor models
(CreditMetrics, KMV)
Industry and
country factors
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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:
f (t )
S (t )  d
 Hedge
instruments:
d
 Hedge ratios: (t )  
 Consider the hedged portfolio:
M (t )  f (t )  (t )' S (t )
 Uncertainty tomorrow  hedge errors:
HE (t  1)  f (t  1)  (t )' S (t  1)  e r  f (t )  (t )' S (t )
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Hedge performance measurement
 Different
hedge strategies (choice of
S and )  different hedge errors.
 1)
 Different models (predict f (t  1), S (t)
different hedge errors.
 Estimate density of hedge errors (risk
profile).
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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
50
Density
40
Model based risk profile
30
20
10
-.7
-.6
Density
20
-.5
-.4
-.3
-.2
-.1
0
.1
.2
.3
.4
.5
.6
.7
-.2
-.1
0
.1
.2
.3
.4
.5
.6
.7
Empirical risk profile
10
-.7
-.6
-.5
-.4
-.3
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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 still
difficult to estimate.

Model risk:Ad hoc and sometimes quite complex.
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