7. Risks of Banking and Risk Mapping

Prof. Dr. Hans-Peter Burghof, University of Hohenheim, Bank Management
7. Risks of Banking and Risk Mapping
Banks face several risks:
Credit risk
Market price risk
o Equity risk
o Interest rate risk
o Currency risk
o Commodity risk
Liquidity risk
Operational risk (containing legal and political risk)
Model risk
Multiple objectives of risk measurement:
Calculation of regulatory capital
Calculation of economic capital
Profit-oriented bank management under risk
Role of the bank supervision regarding the risk management of banks?
190

Prof. Dr. Hans-Peter Burghof, University of Hohenheim, Bank Management
7.1 Pre-Commitment Approach
Intention: Determination of a certain probability of failure F(..) for the bank
without intense intervention
Problem: asymmetric information about the earnings distribution
Solution: “self-regulation“
Bank estimates required equity herself
If losses exceed this amount of capital the bank will be punished
Implementation of F(..) using an incentive-compatible punishment
Possible punishment:
(i) Additional equity requirements in the next period
(ii) Direct monetary penalty
191

Prof. Dr. Hans-Peter Burghof, University of Hohenheim, Bank Management
(i) Additional Equity Requirements
Two points of time 0 and 1
Vt
V=V1–V0
Value of the bank’s portfolio at time t
Change in value of the bank’s portfolio
f(V) Density function of the change in value
F(V) Distribution function of the change in value
r Discount rate (weighted average cost of capital)
Intention: determine the amount of equity KT to implement F(V=-KT)
Supervision can only observe r and sets F(V=-KT)
192

Prof. Dr. Hans-Peter Burghof, University of Hohenheim, Bank Management
Incentive-Compatible Punishment Function
Losses that exceed KT
Punishment -(V + KT)
For every monetary unit of loss > KT the bank has to hold (additional)
monetary units of equity in the next period
Given F(V) Bank minimizes her capital expenditure:
K
T
K T VKTf(
V
) dV
1
r
First order condition (according to Leibniz rule):
0 1
1
r
K
T
1
r
F(
V
K
f ( V
) dV
K
T
given F(
K
T )
T
)
f ( V
) dV
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(ii) Direct Monetary Punishment
Prof. Dr. Hans-Peter Burghof, University of Hohenheim, Bank Management
R bank’s costs of equity, commonly known
Losses that exceed KT
Punishment -(V + KT)
For every monetary unit of loss > KT the bank has to pay a fine of mone-
tary units
Given F(V)
Bank minimizes the sum of cost of (equity) capital and expected fine:
K
T
RK T VKTf( V
) dV
.
1
r
First order condition (according to Leibniz rule):
K
T
0 R f ( V
) dV
1
r
K
T
R1r
given F(
K
) f ( V
) dV
.
F(
V
K
)
T
T
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Prof. Dr. Hans-Peter Burghof, University of Hohenheim, Bank Management
Pros and Cons of the Pre-Commitment Approach
Problem of asymmetric information is resolved
Adequate to control divisions or partial portfolios
Global bank regulation using the pre-commitment-approach?
The punishment has to be credible
Limited liability
Multiple objectives of risk measurement:
Calculation of regulatory capital
Calculation of economic capital
Profit-oriented bank management under risk
Role of the bank supervision regarding the risk management of banks?
195

Prof. Dr. Hans-Peter Burghof, University of Hohenheim, Bank Management
7.2 Actual Supervisory Approach
Bank Management and Bank Supervision Regarding Risk Management
identified risks
relevant risks
measurable risks according
to the state of technology
measurement of
individual risks
banking risks
general supervision of
banking markets
Bagatelle rules
inclusion of new risks
risk measuring requirements
selection of the risk measurement
method
supervisory rules of
risk aggregation
risk aggregation
196
unidentified risks
negligible risks
non-measurable risks
measurement of the total
measurable risk
Potential for additional risk taking, requirement of risk reduction or of additional
equity, sanctions of the bank supervision

Prof. Dr. Hans-Peter Burghof, University of Hohenheim, Bank Management
Overview of Risk Measurement Methods According to Basel I/II
Nontrading
book
institutions
Trading
book
institutions
Risks Captured positions method
Default risks All risky assets (RB)
Market price
risks
Operational
Risk
Default risks
(in the narrower
sense)
RH
Market price
risks
Operational
Risk
All foreign currency positions and raw materials
positions (RH)
Gross profit (all in all or split in business segments),
damage data
197
Standard approach
or IRB
approach (basis/advanced)
Standard approach
or internal risk
models
Basic indicator
approach, standard
approach,
advanced measurementapproach
Risky assets in the banking book (RB) Standard approach
or IRB
Risky
positions
in the trading
book
Italic: Significant changes due to Basel II
Default risks in the banking book
Interest (net
positions)
Stocks (net
positions)
General price risk
Specific price risk
General price risk
Specific price risk
Foreign currency positions and raw material positions
in the banking book and trading book
Gross profit (all in all or split in business segments),
damage data
approach (basis/advanced)
Standard approach
or internal risk
models
Basic indicator
approach, standard
approach,
advanced measurementapproach

Prof. Dr. Hans-Peter Burghof, University of Hohenheim, Bank Management
a) Standard Procedure I: Gearing Ratios for Credit Risks
Default Risk in the Banking Book
Proceedings:
1. Calculation of the assessment basis
Book value, market value
2. Charge rate subject to the expected availment
Globally, for derivatives: market valuation method or duration method
3. Weights of credit ranking
Standard approach: 5 credit ranking classes according to classification: 0%, 20%,
50%, 100%, 150%
(Different weights for special securities or securitizations)
198

Risk Weights for Default Risk
Standard approach:
Risk weights according to external ratings
Prof. Dr. Hans-Peter Burghof, University of Hohenheim, Bank Management
AAA –
AA-
A+ – A- BBB+ –
BBB-
199
External Rating
BB+ –
BB-
B+ – B-
Less
than B-
without
rating
States 0% 20% 50% 100% 100% 150% 100%
Banks option 1 20% 50% 100% 100% 100% 150% 100%
Banks option 2
(short term)
20%
20%
50%
20%
50%
20%
100%
50%
100%
50%
150%
150%
50%
20%
Companies 20% 50% 100% 100% 150% 150% 100%
(Banks option 1: one category worse than the home country)
Problems:
Effects of diversification
Independence of rating agencies
Internal ratings
IRB approach: Risk weights as a function of default probability and other factors

Prof. Dr. Hans-Peter Burghof, University of Hohenheim, Bank Management
b) Standard Procedure II: Building-Block-Approach
Positions with interest rate risks
Risk categories:
Special price risk (idiosyncratic risk)
Weighting factors:
Central states: Special additions to the capital requirement differentiated by duration
and risk categories for rating classes (0% AAA to AA-, 0,25% to 1,60% for A+ to
BBB-, 8% otherwise),
High quality assets:
Up to 6 months 3,125%, 6 months to 2 years 12,5%, more than 2 years 20%.
Other assets: 100%
General price risk (systematic/market risk)
Calculating using maturity method or duration method
200

Maturity Method
Prof. Dr. Hans-Peter Burghof, University of Hohenheim, Bank Management
Weights of closed positions in time bands and zones for maturity method:
Zone/
Band
Weight
(in %)
I/1 -1M 0% 10%
I/2 -3M 0,2% 10%
I/3 -6M 0,4% 10%
I/4 -1J 0,7% 10%
II/1 -2J 1,25% 10%
II/2 -3J 1,75% 10%
II/3 -4J 2,25% 10%
III/1 -5J 2,75% 10%
…
III/6 >20J 6% 10%
Weight of the closed positions
Band Zone Zone I/II
40%
30%
30%
201
40%
Zone
II/III
40%
Zone I/III
Open
positions
150% 100%

Duration Method
Macaulay Duration:
T = Maturity of the security
P = Present value of the security
Prof. Dr. Hans-Peter Burghof, University of Hohenheim, Bank Management
yt = Cash flow of the security at time t
i = Internal rate of return
D
T
t1
T
t1
ty
t
t 1i y
t
1i t
1
P
T
t1
ty
t
t 1i Marginal interest sensitivity of the present value:
P
i
y
t 1
,
T
T
t t t DP D
P
t1
t
mod
t1
1i 1 i t1
1i 1 i
y
202
1

Prof. Dr. Hans-Peter Burghof, University of Hohenheim, Bank Management
Weights of closed positions in time bands and zones for duration method:
Zone/
Band
Change
of return
(in %)
I/1 -1M 1.0% 5%
I/2 -3M 1.0% 5%
I/3 -6M 1.0% 5%
I/4 -12M 1.0% 5%
II/1 -1.9J 0.9% 5%
II/2 -2.8J 0.8% 5%
II/3 -3.6J 0.75% 5%
III/1 -43J 0.75% 5%
…
III/8 >20J 0.6% 5%
Weight of the closed positions
Band Zone Zone I/II
40%
30%
30%
203
40%
Zone
II/III
40%
Zone I/III
Open
positions
150% 100%

Prof. Dr. Hans-Peter Burghof, University of Hohenheim, Bank Management
Internal Models and Value at Risk
Qualitative specifications:
1. Work organization and process organization
2. Risk controlling
3. Documentation
4. Continuous check of the risk models
5. Calculation of crisis scenarios
6. Daily limitation of risk
7. Updated historical data base
8. Annual inspection by the internal audit
9. Responsibility of the management
204

Prof. Dr. Hans-Peter Burghof, University of Hohenheim, Bank Management
Quantitative and Methodical Specifications:
3. Value at Risk
Standardization of the lower partial moment of 0 th order
K
Ky n
LPM ( n,
K)
df ( y)
, with n = 0
LPM ( 0,
K)
F(
y K)
Confidence level
K = VaR
2. Confidence level 99%, holding period 10 days
3. Global triplication of the required equity
y = Difference between the actual terminal value
of the portfolio and the terminal value of
the previous period
VaR (p)
(Confidence
level of p
percent)
3VaR (p) = VaR (q) (Confidence level of q
percent)
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y=0
f(y)
y

Feedback through Backtesting:
Prof. Dr. Hans-Peter Burghof, University of Hohenheim, Bank Management
Backtesting
Period under review: 250 business days
Number of overshoots (in %) Additional factor
< 5 ( 9 (> 4%) 1
206

Literature for Chapters 7
Prof. Dr. Hans-Peter Burghof, University of Hohenheim, Bank Management
Burghof/Henke (2000): Kreditderivate und Bankenaufsicht – Entwicklungen und Perspektiven
in Deutschland und international, in: Burghof et al. (Hrsg.): Kreditderivate.
Hartmann-Wendels/Pfingsten/Weber (2000): Bankbetriebslehre,
insbes. Kapitel H, I.
Krümmel (1989): Unternehmenspolitische Vorgaben für die Risikosteuerung der Bank, in:
Krümmel/Rudolph (Hrsg.):Finanzintermediation und Risikomanagement.
Schierenbeck (2001): Ertragsorientiertes Bankmanagement.
207