Prof. Dr. Hans-Peter Burghof, University of Hohenheim, Bank Management
5. Profit-Oriented Bank Management
5.1 Systems of Bank Calculation and Bank Management
Perspectives and Methods of Bank Management
Perspective
Maximization of return
Limitation of risk
E(x) max!
R<X
Bank calculation
- Interest margin calculation
- Marktzinsmethode
Documentation
Planning
- Cost accounting
- Other risk measures
Management of single
transactions, portfolio
management, incremental
Value at Risk
Management of single
transactions, floor prices
Internal transfer prices,
budgeting or internal
markets for company resources
- Measures of downside
risk, esp. Value at Risk
Management
Profit-oriented incentive
systems
Internal transfer price,
limiting systems or internal equity markets
Sanction in case of violation of limits
Controlling
division
Controlling
Risk management,
Treasury
Management of the entire bank with
risk adjusted performance measures
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Prof. Dr. Hans-Peter Burghof, University of Hohenheim, Bank Management
5.2 Fundamentals of Bank Calculation
Tasks of bank calculation (Pfingsten et al., p. 629):
 Documentation
 Preparing data for planning purpose
 Provision of crucial information
 Management of decision makers’ behavior
 Controlling of business processes
“Wertbereich” versus “Betriebsbereich” in business and bank calculation
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Prof. Dr. Hans-Peter Burghof, University of Hohenheim, Bank Management
“Wertbereich” versus “Betriebsbereich” in the
Contribution Margin Calculation
Contribution margin calculation
interest earnings
-
interest expense
=
customer interest contribution (“Konditionsbeitrag”) (section 5.3, 5.4)
-
risk costs (section 5.5.1)
=
contribution margin I (“Wertbereich”)
+ / - directly attributable commissions (section 5.5.2)
=
contribution margin II (“Wertbereich” and commission income)
+ / - attributable operating revenues and costs (section 5.5.2)
=
contribution margin III (market-related business performance)
Calculation of single deals/transactions (section 5.6)
aggregation
(section 5.7)
Management of the entire bank (section 5.8)
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Prof. Dr. Hans-Peter Burghof, University of Hohenheim, Bank Management
5.3 Traditional Methods to Calculate the Net Interest Income
Interest Obligation Balance
Vol.
(mio.)
15
Ø interest
0%
Revenues
(mio.)
Position
0
Unlimited
maturity
(real estate,
buildings)
Equity
Debt with
fixed interest period >
10 years
Position
Expenses
(mio.)
Ø interest
Vol.
(mio.)
0
0%
12
1.4
7.0%
20
15
8.5%
1.275
Loans with
fixed interest period
> 10 years
12
8.3%
0.996
9.5-10 years 9.5-10 years
0.408
6.8%
6
18
8.1%
1.458
9-9.5 years
0.536
6.7%
8
…
…
…
…
…
…
…
…
30
6.1%
1.83
0.5- 1 year
0.5 - 1 year
2.2
4.0%
55
Sum of all
Sum of all
liabilities
assets with
with fixed
fixed rate of
rate of interinterest
est
9.12
5.7%
160
Overdraft
credits
Short-term
deposits
4.05
4.5%
90
Total assets
Total liabilities
190
7.1%
13.49
60
10.5%
6.3
250
19.79
9-9.5 years
13.17
Objectives:
- Calculation of the net interest income
- Identification of the interest rate risk (risk of interest rate changes)
143
250
Prof. Dr. Hans-Peter Burghof, University of Hohenheim, Bank Management
Pooling Method versus “Schichtenbilanzmethode”
Pooling method:
The interest reference rate is the average interest rate of the other side of the balance sheet, respectively
“Schichtenbilanzmethode”:
The interest reference rate is the average interest rate of a (in terms of liquidity
and profitability) comparable “Schicht” of the opposite side of the balance sheet
Critical review of both methods:
Objective inconsistency:
 Refinancing actually under different conditions
 Twofold attribution of the margin to lending and deposit business or random distribution
Temporal inconsistency:
 The interest reference rate changes over time
 The Structure of the “Schichtenbilanz” and the pool change over time
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Prof. Dr. Hans-Peter Burghof, University of Hohenheim, Bank Management
Example of Pooling Method and “Schichtenbilanzmethode”
Loans with a fixed period of interest of 9.2 years: 7.9%
For the interest obligation balance see slide 35
Pooling method:
Interest reference rate as average interest rate of liabilities:
(160/250)*5.7% + (90/250)*4.5% = 5.268%
margin: 7.9% - 5.268% = 2.632%
“Schichtenbilanzmethode”:
Comparable “Schicht”, e.g. financial assets with comparable fixed interest
rate, in this example 9 - 9.5 years: 6.7%
margin: 7.9% - 6.7% = 1.2%
Twofold attribution of the margin to lending and deposit business?
Adjustment in the example:
Pooling method:
Average interest rate of assets
(190/250)*7.1%+ (60/250)*10.5%=7.916%
Gross interest spread of the whole balance sheet: 7.916%-5.268%=2.648%
Margin of the loan: 2.632%-0.5*2.648=1.308%
“Schichtenbilanzmethode”:
Gross interest spread 9 – 9.5 years: 8.1% - 6.7%= 1.4%
Margin of the loan: 1.2%- 0.5*1.4%= 0.5%.
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Prof. Dr. Hans-Peter Burghof, University of Hohenheim, Bank Management
5.4 Marktzinsmethode
5.4.1 Basic Idea
Identification of sources of success in banking calculation
Requirements:
The bank has access to a perfect capital market (that is, complete and perfectly
competitive)
Completeness:
Every new financial asset can be replicated with already existing financial assets
Perfect competition:
Banking transactions can be replicated frictionless on the capital market
In the equilibrium of a perfect market: additivity property and absence of arbitrage and
E.g.: Two-period loan
t0
t1
t2
?
=
b
Replication with two zero-coupon bonds
t1
t2
t1
t2
+
a
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Prof. Dr. Hans-Peter Burghof, University of Hohenheim, Bank Management
Interest Rate, Fixed Period of Interest and Success in Banking
Key source of success in the banking business: interest income
Yield curves as a function of fixed interest rates:
7,0%
normal yield curve
6,0%
inverse yield curve
5,0%
flat yield curve
4,0%
3,0%
2,0%
1,0%
0,0%
1 year

2 years
3 years
4 years
5 years
6 years
7 years
The sources of success for the interest rate business:
- Customer interest contribution (“Konditionsbeitrag”):
Difference to the interest reference rates with the same maturity
- Mismatch contribution (“Strukturbeitrag”) (?):
Difference between market interest rates with different maturity
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Prof. Dr. Hans-Peter Burghof, University of Hohenheim, Bank Management
Customer Interest Contribution and Mismatch Contribution
(In the Basic Concept of the Markzinsmethode I)
Clients
Clients
Bank
Lending business with clients
Deposit business
with clients
Calculation of the
customer interest contribution
Hypothetical
alternative investment on the
capital market
Calculation of
the mismatch
contribution
Hypothetical
alternative investment on the
capital market
Perfect capital market
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Prof. Dr. Hans-Peter Burghof, University of Hohenheim, Bank Management
Numerical Example:
Customer Interest Contribution and Mismatch Contribution
Bank Balance Sheet
[in mio.]
customer debit market
interest interest interest
contr.
rate
assets
liabilities
market credit customer
interest interest interest
rate
contr.
0.6%
4.1%
3.5%
Acceptance
credit (1 year)
100
Saving deposit
(3 months)
140
3.2%
2.5%
0.7%
3.7%
8.9%
5.2%
Consumer credit
(3 years)
80
Savings bond
(3 years)
90
5.2%
4.5%
0.7%
1.3%
7.5%
6.2%
Mortgage loan
(7 years)
140
Bond
(5 years)
90
5.8%
6.1%
-0.3%
1.68%
6.79%
5.11%
4.49%
4.08%
average weighted interest rate
interest reference rate for
mismatch contribution 3.2%
1.91%
mismatch mismatch
contr. assets contr. liabilities
mismatch contribution:
0.61%
customer interest contribution: 2.1%
149
-1.29%
0.42%
Prof. Dr. Hans-Peter Burghof, University of Hohenheim, Bank Management
5.4.2 Calculating a Single Deal Using Marktzinsmethode
Replication of a Loan with Other Assets
Loan: 2 years to maturity, 100 monetary units, 6%, retrospective interest payment and amortization, 50% amortization p.a., (no default risk)
Other (default risk free) assets on the money and capital market:
Coupon bond 1:
1 year, 3.5%, quoting at par
Coupon bond 2:
2 years, 4.5%, quoting at par
t0
t1
t2
-100
56
53
Coupon bond 2
(2 years, 4.5%)
-53/1.045
= -50.72
50.72*4.5%
= 2.28
53
Coupon bond 1
(1 year, 3.5%)
-53.72/1.035
= -51.90
56-2,28
= 53.72
2.62
0
Credit: 6%
Difference =
Net present value
150
0
Prof. Dr. Hans-Peter Burghof, University of Hohenheim, Bank Management
Intertemporal Allocation of the Net Present Value (NPV)
First step: Calculation of arbitrage-free discount factors using capital market
prices (here: coupon bond 1 and 2)
These discount factors can be interpreted as prices of normalized zero bonds (a
normalized zero bond pays exactly 1 monetary unit at maturity). The price of a
normalized zero bond in t0 is called ZB0,t, where t is the time to maturity.
Coupon bond 1 is identical to a 1-year zero bond, thus: ZB 0,1  1 / 1.035  0.9662 .
The arbitrage-free price of the 2-year zero bond results from replication:
t0
t1
t2
Coupon bond 2
(2 years, 4.5%)
-100
4.5
104.5
Zero bond (0,2)
104.5* ZB0,2
-
-104.5
Zero bond (0,1)
4.5*ZB0,1
= 4.3478
-4.5
Difference =
Net present value
!
0
0
100  104.5  ZB 0, 2  4.5  ZB 0,1  ZB 0, 2  0.9153
151
0
Prof. Dr. Hans-Peter Burghof, University of Hohenheim, Bank Management
i) Effective Customer Interest Contribution Margin
Calculation of the annuity pursuant base on the basis of the effective capital
t0
Capital base
Discount factor
Present value of the
capital base
Annuity pursuant
base
t1
t2
100
50
0,9662
0.9153
0.9662*100
= 96.62
0.9153*50
= 45.77
142.39
Effective customer interest contribution margin = 2.62/142.39 = 1.84%
Annuity pursuant of the customer interest contribution on the basis of the effective customer interest contribution margin
t0
t1
t2
100
50
Annuity
1.84%*100
= 1.84
1.84%*50
= 0.92
Present value of the
annuity
0.9662*1.84
= 1.78
0.9153*0.92
= 0.84
Capital base
NPV
2.62
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Prof. Dr. Hans-Peter Burghof, University of Hohenheim, Bank Management
ii) Annuity Pursuant for Capital Congruent Refinancing
For coupon bonds quoting at par:
t0
t1
t2
-100
50
50
6
3
Loan:
Capital (re)payment
Interest payment
Refinancing: coupon
bond 1 (1 y., 3.5%):
Capital (re)payment
50
-50
Interest payment
-3.5%*50 = -1.75
Refinancing: coupon
bond 2 (2 y., 4.5%):
Capital (re)payment
50
Interest payment
0
-50
-4.5%*50 = -2.25
-4.5%*50 = -2.25
Capital difference
0
0
0
Interest difference
0
2
0.75
0.9662*2
= 1.93
0.9153*0.75
= 0.69
Present value of the
interest surplus
2.62
Arbitrarily distribution of the NPV across the single periods?
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Prof. Dr. Hans-Peter Burghof, University of Hohenheim, Bank Management
5.4.3 Mismatch Contribution and Interest Rate Risk
Concept of period transformation:
Short-term financing (cheap) and long-term investment (expensive)
Premise: Normal yield curve
Is it possible to earn a profit doing period transformation solely?
Idea:
Replication of the basic business using short-term forward contracts
 No interest rate risk due to changing refinancing condition
Credit: 6%
t0
t1
t2
-100
56
53
53
1  i1, 2
-53
Refinancing in the
second period (1
year, i1,2)
Refinancing in the
first period (1 year,
3.5%)
Difference =
NPV
56 
53
1  i1, 2

53
  56 
1  i1, 2

1  i 0,1
56 
53
1  i1, 2
1  i 0,1
 100
Calculation of the forward rate i1,2?
154




Prof. Dr. Hans-Peter Burghof, University of Hohenheim, Bank Management
Absence of Arbitrage on the Capital Markets
 The forward rate is calculated so that the value of a multi-period investment
equals the value of a repeated short-term (forward) investment
(Otherwise a risk-free profit (arbitrage) is possible by taking a short position in
the more valuable investment and a long position in the other one)
Cash flow
at time t
2-year investment
with reinvestment of interest earnings
Investment
t0
-1
t1
-i0,2
Interest and amortization
Revolving 1-year investment
Investment Interest and amortization
-1
i0,2
-(1 + i0,1)
(1 + i0,2) + i0,2(1 + i1,2)
t2
(1 + i0,1)
(1 + i0,1)(1 + i1,2)
1  i   i 1  i   1  i 1  i 
0, 2
0, 2
1, 2
0 ,1
1, 2
 1  i0, 2   1  i1, 2 1  i0,1  i0, 2 
 i1, 2 
1  i0 , 2
1  i0,1  i0, 2
1 
1  4.5%
 1  5. 5 %
1  3.5%  4.5%
(Notice to calculate with the correct interest rates esp. if coupon bonds do not quote at par!)
 Alternative and maybe easier way to calculate the forward rate: arbitrage
strategy with zero bonds.
53
1  0.0 5  100  2.62
1  0.035
56 
NPV of the whole transaction in the example above:
NPV of the customer interest contribution: 2.62  Mismatch contribution: 0
 An ex post positive mismatch contribution is the result of interest rate speculation!
Consequences for banking policy?
155
Prof. Dr. Hans-Peter Burghof, University of Hohenheim, Bank Management
5.5 Some More Components of the Contribution Margin Calculation
5.5.1 Costs of Risk
Standard risk-costs versus real risk premium
2
1
E(x)
Appointed
repayment sum
1 Standard risk-costs of the portfolio, covered by (credit) terms
Charged to the amount of the expected loss
2 Variation of the earnings, covered by equity
Charged to the amount of the additional costs for the required economic
or regulatory (equity) capital
156
Prof. Dr. Hans-Peter Burghof, University of Hohenheim, Bank Management
5.5.2 Revenues and Costs of the Operating Sector
Revenues:
Provisions and charges
Costs:
Problem of attribution out of a technical perspective
Problem of attribution out of an operational perspective
Solution in banks:
Activity based costing (process-oriented calculation of standard direct costs)
157
Prof. Dr. Hans-Peter Burghof, University of Hohenheim, Bank Management
Example: Standard Costs per Unit of a Small Loan (2-Years to Maturity)
Personnel expenses
Operation
Preliminary talk
Application handling
Account opening
“Schufa” information
Loan folder creation
Account analysis
Data processing costs
Operation
Account opening/closing
Account management
Account closure
Unit per
loan
1
1
1
1
1
8
Minutes per
unit
20
30
10
5
10
8
Costs per
minute
3.25
1.90
1.90
1.90
1.90
2.10
Standard costs per
unit
65
57
19
9.50
19
134.40
303.90
Unit per
loan
2
24
2
Seconds per
unit
0.3
0.3
0.5
Costs per
second
2.50
2.50
2.50
Standard costs per
unit
1.50
18
2.50
22
Units per
loan
1
1
1
1
1
8
Costs per
unit
0.40
0.20
0.20
1.45
0.15
1.00
Standard costs per
unit
0.40
0.20
0.20
1.45
0.15
8
10.40
Other material expenses
Material
Application form
Form on provision of collateral
“Schufa” information
Loan folder
Loan confirmation form
Postal charges
Sum = Standard costs per unit of a small loan
336.30
(see Schierenbeck, p. 369)
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Prof. Dr. Hans-Peter Burghof, University of Hohenheim, Bank Management
5.6 Single Transaction Calculation as Contribution Margin Calculation
Gross contribution margin
(Actual contribution margin I)
- Margin of standard risk costs
= Net contribution margin
- Standard operating expenses margin less provision margin
= Total net contribution margin II
(Actual contribution margin II)
- Debit contribution margin for operating expenses and equity
= Excess profit/deficit
(Actual contribution margin III)
(see Schierenbeck, p. 370)
Each in percent of the present value of the particular cash flows relating to the
present value of the average credit/investment volume
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Prof. Dr. Hans-Peter Burghof, University of Hohenheim, Bank Management
5.7 Aggregation of Results for Banking Management
Ways of Aggregation
Calculation of business transaction/
Account calculation
Calculation of the clients
consultant
Product
Client
calculation
calculation
Product line
Client group calculation
Calculation of a profit
center
calculation
Calculation of a branch
from one district
Aggregation to the
performance of client business
Profit center
Product type
calculation
calculation
Accounting and client
calculation
(see Schierenbeck, p. 399-403)
160
Prof. Dr. Hans-Peter Burghof, University of Hohenheim, Bank Management
Objectives of the Different Calculation for Controlling
Profit center calculation:
Product type calculation:
Account and client calculation:
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Prof. Dr. Hans-Peter Burghof, University of Hohenheim, Bank Management
5.8 Global Bank Management
Differentiated presentation of the bank’s performance:
Market performance
(client business)
Customer interest contribution
- standard costs of risk
+ commission earnings
- standard operating expenses
Risk performance
(client business)
Standard costs of risk
- Actual costs of risk
Operating performance
(cost units)
Standard operating expenses
- Actual operating expenses
Client business performance
+
Trading performance
Treasury performance
Contribution of trading income
- direct costs of the trading
section
Contribution of treasury income
- direct costs of
treasury activities
Investment performance
Performance of investing
central positions
- direct costs respectively
opportunity costs of central
positions
Central performance
- Overheads
= Operating income of the entire bank
+ Other and extraordinary earnings
= Net earnings of the entire bank
(see Schierenbeck, p. 407)
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Prof. Dr. Hans-Peter Burghof, University of Hohenheim, Bank Management
ROI Scheme
Gross interest margin
1,7%
Provision
margin
0.9%
Gross earnings margin
3.2%
Return on
equity after
taxes
Return on
equity before
taxes
10%
20%
Gross profit
margin
Trading margin
1.3%
0.5%
Net profit
margin
AOSE margin
1.0%
0.1%
Risk margin
Tax ratio
Personnel
expenses
margin
-0.3%
50%
1.2%
Equity ratio
Gross requirements
margin
5.0%
1,0%
Material
costs margin
0.7%
(see Schierenbeck, p. 421)
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Prof. Dr. Hans-Peter Burghof, University of Hohenheim, Bank Management
Benchmark for Ratios
1. Transaction volume
Compensated or uncompensated balance sheet?
Average or reporting date balance sheet?
Inclusion of off-balance positions?
2. Equity
Balance sheet equity
Liable equity
164
Prof. Dr. Hans-Peter Burghof, University of Hohenheim, Bank Management
Literature
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.
165