Performance-Messung - Goethe

Transcription

Schwerpunkt Finanzen
Johann Wolfgang Goethe Universität, Frankfurt (Main)
Prof. Dr. Mark Wahrenburg
und Dr. Peter Raupach
Commercial Banking
Performance Measurement & Capital Allocation
4-stündige Vorlesung mit Übung im SS 2002
Commercial Banking - Prof. Wahrenburg
1
Purpose and objectives
Purpose
Objectives
Understand techniques to optimize the risk-return
trade-off of the bank
Understand, how capital allocation can steer the bank
Understand Pros/Cons of different approaches
- ROA/ROE
- RAROC/RORAC
Understand tasks & instruments of risk controlling unit
2
Capital allocation = Socialism?
“The problem is to construct a system of information, accounting,
economic indices and stimuli which permit local decision-making
organs to valuate the advantage of their decisions from the point of
view of the whole (firm)”…[objective just like capital allocation!]
“The hard thing in a model realization is to receive and often to construct
necessary data which in many cases have considerable errors and
sometimes are completely absent, since none needed them
previously.”
Leonid V. Kantorovich, U.S.S.R.
Rede Nobelpreisverleihung 1975
3
Conflicting objectives
RAROC: Maximize risk adjusted return per unit of economic capital
• Prevent regulatory capital shortage
• Optimize taxes
• Maximize EPS / RoE
• Optimize bank rating, minimize prob of bank default
• Keep cash reserves for akquisitions
• Execute strategic bank development plan
4
Why economic capital?
“What we generally call profits, the money left to service equity, is
usually not profits at all. Until a business returns a profit that is greater
than the cost of capital, it operates at a loss.”
Peter Drucker
• EVA, Shareholder Value, ROE all are based on a definition of equity
capital employed
• Without an adequate definition of equity for every business unit, we
cannot differentiate success/failure from a shareholder perspective
5
Why not use regulatory capital?
Too little differentiation of risk
• today AAA-corporates and junk bonds all consume the same
regulatory equity!
Some business units do not require regulatory equity at all
• Example: interest rate risk taking in the banking book
Risk perception of shareholders, not regulators, sets return
targets
6
Objectives of capital allocation
Protection of
the bank
Efficient
allocation
of resources
Risk based
pricing
How much
capital
needed?
What business
units shall
expand?
How to price
transactions?
7
What exactly is the „capital“ to be allocated?
Cash
Credit Line
useless, because
is does not restrict
volume of derivatives,
guarantees etc.
Regulatory
Capital
still too often used
today
can be poor measure
of actual risks
Economic capital
Risk capital
Value at Risk
all terms have same
meaning
defines today‘s state
of art
8
Evolution of performance measures
Example: calculating a loan
Loan amount
Reg. equity
Econ. capital
ROA
return on assets
Loan ROA
100 (10 % − 2 % − 6 %)
100
= 2%
Exp. loses
Loan rate
Refinance rate
100 €
8€
12 €
2%
10%
6%
ROE
return on (regulatory)
equity
RORAC
return on
economic capital
Loan ROE
Loan RORAC
100(10% − 2%) − 92 * 6%
8
= 31%
100(10% − 2%) − 88 * 6%
12
= 22, 6%
9
Probability of
losses
Economic Capital: A universal concept
confdence level 99%
1% probability
Reserve
No Loss
0%
expected
loss
Catastrohe losses
Losses captured by
economic capital
default rate
100%
10
RORAC is able to encompass all sources of risk
Total
VaR
Credit
VaR
Market
VaR
Operational
VaR
today: simple adding up of VaR numbers
future: Integration of market and credit risk in order to model
dependencies
11
RORAC is an universal evaluation tool on all business
levels
Overall Bank
RORAC
Buiness Unit
RORAC
Client
RORAC
Product
RORAC
Transaction
RORAC
12
RORAC makes performance of all business units
comparable
RORAC
Unit
1
2
3
4
5
6
7
8
9
Capital
10
15
40
20
30
15
20
70
80
Excess
Returns
3
4
8
10
5
3
2
8
5
9
RORAC
30%
27%
20%
50%
17%
20%
10%
11%
6%
7
5
3
1
0%
10%
Value
destruction
20%
30%
40%
50%
60%
Value
creation
Hurdle rate required by
shareholders
13
RORAC / RAROC have set today‘s market standards
Ex Ante Analysis: RORAC = Return on Risk Adjusted Capital
RORAC =
expected profit
economic capital
Ex Post Analysis: RAROC = Risk Adjusted Return on Risk Adjusted Capital
RAROC =
realized profit - hurdle rate
economic capital
14
Do not trust RARAOC alone: some basic problems
1.Differentiate good luck from superior ability
• Is 30% return on a stock portfolio good or bad?
• Does profit from maturity mismatches in ALM demonstrate superior ability?
• Is 2% realized loses on loans with 3% standard risik costs outperformance?
2. Allocation of other costs to business units / products
• How allocate cost of „Corporate Center“ (IT, accounting, Planning)?
• How allocate cost of maintaining the branch network?
• How allocate cost of maintaining a payment system
3. Cross subsidization between products
• Would you close down a credit business with bad RAROC, if this business is
necessary for receiving profitable M&A deals?
15
A rigorous foundation of RAROC*
K: Buchwert Kredite
D: Buchwert Einlagen
EK M : Marktwert des Eigenkapitals
EK B : Buchwert des Eigenkapitals
EL : erwartete Ausfallrate (in % des Kreditvolumens)
EL: realisierte Ausfallrate (in % des Kreditvolumens)
RK : Risikokapital bzw. VaR
erwartetes Nettoergebnis der Bank = K ( rK − EL) − D rD
"erwarteter Jahresüberschuss vor Steuern"
rf : sicherer Zins bzw. Refinanzierungszins
rK : Kreditzins
rD : Einlagenzins
rE : Rendite des EK bzw. Eigenkapitalkostensatz
EKK : Eigenkapitalkosten = EK M * rE
* Lit:
H. Schierenbeck,
Ertragsorientiertes
Bankmanagement
16
Performanceanalyse einer risikolosen Bank
Re nditeforderung des EK : rf
Eigenkapitalkosten = EKK = EK M rf
Erwartetes Nettoergebnis (vor EKK) = K (rK − EL) − D * rD
= K (rK − EL − rf ) + D ( rf − rD ) + EK B * rf
(Bilanzidentität : K = D + EK B )
⇒ Kapitalkosten erwirtschaftet, wenn :
Nettoergebnis > EKK , bzw :
K (rK − EL − rf ) + D ( rf − rD ) + EK B * rf
= rf
EK M
" Ziel − ROE der sicheren Bank "
17
Ex post Performanceanalyse risikolose Bank
K (rK − EL − rf ) + D ( rf − rD ) + EK B rf
= rf
EK M
K (rK − L − rf ) + D ( rf − rD ) + EK B rf
EK M
" Ziel − ROE der sicheren Bank "
" Re alisierter ROE"
Realisierte Überrendite des EK über die EK-Kosten
RAROC = Real. ROE - Ziel-ROE
18
Renditeforderung riskante Bank
(
)
(
Wertpapiermarktlinie CAPM: rE = rf + rM − rf β E = rf + rM − rf
)
σ E ρ E,M
σM
Definition Risikokapital: RK=VaR = α σ E EK M
(
)
EKK Bank = EK M  rf + rM − rf β i 


= EK M rf +
(
(r
)
− rf ρ i ,M
M
ασM
)

rM − rf ρ i ,M
=  rf +

ασM

Ziel: EKK als Funktion des
RK ausdrücken
RK

 RK + ( EK M − RK ) rf


Ziel-RORAC: geforderte Rendite pro
Einheit Risikokapital
19
Zahlenbeispiel
EK MW : 1 Mio
RK = 3*20%*1 Mio. DM=600 000 DM
σ i : 20%
σ M : 20%
ρ i,M : 1
Ziel-RORAC= rf +
(r
M
)
− rf : 7%
(r
M
)
− rf ρ i,M
ασM
= 5% +
7%
= 16, 6%
3 * 20%
rf : 5%
α :3
20% * 1 

EKK=1Mio.  5% + 7%

20% 

= 120 000DM
EKK=RK*RORAC+(EK MW − RK ) * rf
= 600 000DM * 16, 6% + (1Mio − 0, 6Mio.) * 5%
= 100 000 DM+20 000 DM=120 000 DM
20
Erwirtschaftet Bank ihre Eigenkapitalkosten?
erwartetes Nettoergebnis ≥ EKK ?
K (rK − EL − rf ) + D ( rf − rD ) + EK B * rf ≥ RK * Ziel-RORAC + (EK MW − RK ) * rf ?
bzw. :
K (rK − EL − rf ) + D ( rf − rD ) + EK B * rf − (EK MW − RK ) * rf
≥ Ziel-RORAC?
RK
21
Anwendung: RAROC einer Kreditbank
EK B : 1 Mio. DM
EK M : 1 Mio. DM
K: 10 Mio. DM
D: 9 Mio. DM
rK : 7, 5%
EL : 1%
rD : 4,5%
rf : 5%
RK: 600 TDM
Ziel-RORAC: 16,6%
erwartetes Nettoergebnis :
10 Mio. (7,5%-1%-5%) +9Mio. (5%-4,5%) + 1 Mio. *5%
= 150 TDM + 45 TDM + 50 TDM = 145 TDM
245 TDM-(EK M − RK )rf 225 TDM
=
= 37, 5%
RK
600 TDM
> Ziel − RORAC = 16, 6%
erwarteter RORAC =
Re alisierte Ausfallrate: 1,5%
195 TDM-(EK M − RK )rf 175 TDM
Realisierter RORAC=
=
= 29, 16%
RK
600 TDM
RAROC = Real. RORAC - Ziel-RORAC = 29, 16% - 16,6% = 12,5%
22
Conclusion
We must differentiate 3 risk adjusted return concepts:
Target-RORAC
hurdle rate that must be earned in order to earn cost of equity
depends on:
- cost of equity (beta factor of bank within CAPM)
- difference between market value of equity and economic capital
Expected RORAC
calculated with expected losses
Realisized RAROC
calculated with realized loses
23
Bottom Up estimation of economic capital
OUTSTANDINGS ($000)
x
Risk Remaining Tenor (Years)
Grade Demand
1
1
(1,697)
(20,193)
2
0
194,830
3
686
853,557
4
(675)
479,472
5
0
52,334
6
0
62,421
7
0
40,474
8
3,671
0
9
0
0
10
0
0
NA
240
226,006
Total $
2,224 $ 1,888,901 $
4
2,535
1,125
606
1,969
667
0
0
0
0
0
15,380
22,282
5
6
7
8
9
10
0
781
10,521
3,928
0
293
182,000
0
0
0
2,960
$ 200,482
0
0
4,093
0
53
0
0
0
0
0
19,371
$ 23,516
0
0
0
0
0
0
0
0
0
0
3,820
$ 3,820
0
2,080
172
0
0
0
0
0
0
0
8,675
$ 10,927
0
0
0
0
0
0
0
0
0
0
3,605
$ 3,605
0
0
0
0
196
0
0
0
0
0
29,688
$ 29,883
9
10
90
210
368
775
925
1,050
1,000
1,900
3,300
4,500
850
Total
(16,698)
215,856
900,906
532,667
57,844
62,966
222,474
3,703
0
0
221,961
$ 2,201,679
CAPITAL FACTORS (bps)
Grade Demand
1
1
13
13
2
20
20
3
45
45
4
181
181
5
271
271
6
500
500
7
1,000
1,000
8
1,900
1,900
9
3,300
3,300
10
4,500
4,500
NA
226
226
=
2
3
0
2,659
16,557
482
25,025
6,247
28,782
19,192
4,595
0
253
0
0
0
0
32
0
0
0
0
22,487 (110,271)
97,699 -$ 81,660 $
2
3
4
5
6
7
8
18
35
68
300
429
700
1,000
1,900
3,300
4,500
365
25
50
92
363
517
850
1,000
1,900
3,300
4,500
440
33
65
119
426
596
950
1,000
1,900
3,300
4,500
511
40
85
181
500
667
1,000
1,000
1,900
3,300
4,500
583
48
100
225
588
758
1,050
1,000
1,900
3,300
4,500
673
55
120
270
675
842
1,050
1,000
1,900
3,300
4,500
758
68
150
317
725
883
1,050
1,000
1,900
3,300
4,500
804
78
180
343
731
883
1,050
1,000
1,900
3,300
4,500
807
REQUIRED CAPITAL for OUTSTANDINGS ($000)
Grade
Demand
1
1
(2)
(25)
2
0
390
3
3
3,841
4
(12)
8,690
5
0
1,417
6
0
3,121
7
0
4,047
8
698
0
9
0
0
10
0
0
NA
5
5,109
Total $
692 $
26,590 $
2
3
0
7
58
2
171
57
863
696
197
0
18
0
0
0
0
6
0
0
0
0
820
(4,847)
2,127 -$ 4,079 $
4
8
7
7
84
40
0
0
0
0
0
786
932
$
5
6
0
7
190
196
0
29
18,200
0
0
0
173
18,795
0
0
92
0
4
0
0
0
0
0
1,304
1,400
$
7
$
8
0
0
0
0
0
0
0
0
0
0
290
290
$
9
0
31
5
0
0
0
0
0
0
0
698
734
$
10
0
0
0
0
0
0
0
0
0
0
291
291
$
0
0
0
0
18
0
0
0
0
0
2,523
2,542
Total
$
(12)
495
4,367
10,518
1,676
3,168
22,247
704
0
0
7,151
50,314
24
Quite often, due to data availability problems, economic
capital is estimated as a function of expected loss
Typical Capital as a Function of Expected Annual Loss in
Consumer (Basis Points)
1,200
1,000
800
600
400
200
0
0
500
1,000 1,500 2,000 2,500 3,000 3,500 4,000 4,500 5,000
Expected Loss
25
CAPM vs. RAROC perspective
CAPM
RAROC
Cost of equity according to CAPM
target return on economic capital
ri = r f + ( rM − r f ) ßi
rf
Risk, measured by ßi:
σ i,M
σ M2
What risk contribution to diversified
portfolio?
VaR = α * PV * σ i
σi
What contribution to probability of
extreme losses / of default ?
26
RAROC is closely related to Sharpe Ration
Sharpe Ratio
E(R)
•
Sharpe Ratio =
CAPM Capital market line
•
R i = rF + (rM − rF )
σi
σM
Ri − rF
σi
σi
Gilt nach CAPM nur für effiziente Portfolios!
27
However, CAPM tells us that single positions should be
evaluated by security market line
E(R)
Profit Center 1
•
•
} Jensens α
CAPM Security market line
Ri = rF + (rM − rF )β i
Profit Center 2
rF
ßi
28
Is RAROC consistent with CAPM?
Example: An asset has a CAPM-beta of 0
Æ expected return (hurdle rate) according to CAPM = rf
RAROC: Compensation for economic capital required, if
position affects bank VaR
Æ required return > equilibrium return in capital market
A trader who „beats the market“ does not neccessarily produce
a positive RAROC
29
RAROC with „isolated“ VaR vs. „contribution to total bank
VaR“
Re turn
RAROC1 =
VaR der Position
RAROC 2 =
Re turn
VaR − Beitrag der Position
Each business unit optimizes own
risk position only
Æaccounts for correlation
with other business units
Æ Incentive to optimize total
bank portfolio
30
Periodenzurechnung des Ergebnisses aus Kreditgeschäft
Beispiel: Endfälliger risikoloser Kredit
Konditione nbeitragsb arwert = −(100 - Disagio) +
Zins
Zins
100 + Zins
+
+ ... +
1+ r1 (1+ r2 ) 2
(1+ rT )T
• = NPV des Kredits
• Abzinsung mit laufzeitkongruenten
Zerozinssätzen
Interpretation a): NPV kann in t0 als
Dividende entnommen werden
Interpretation b): NPV kann als
Dividendenstrom entnommen werden. Æ wie
hoch ist die Dividende pro Periode?
31
Periodenzurechnung des Konditionenbeitragsbarwert
Alternative a) Welche Annuität kann aus NPV gezahlt werden?
Alternative b) Welche Rendite des (jeweils) gebundenen Kapitals kann aus
NPV pro Periode gezahlt werden? (KBBW)
i −1
gebundenes Kapital in t i = Nominalwer t − ∑ Tilgungk
k =1
Beispiel zur Verrentung der Konditionsmarge
Zeitpunkt
(1)
Gebundenes Kapital
(2)
Konditionsmarge
(3)
Rente (1)*(2)
(4)
Abzinsungsfaktoren
(5)
Barwerte (3)*(4)
(6)
KB-Barwert (Summe(5))
0
1
2
100
50
3,34%
3,34%
3,34
1,67
0,943
0,873
3,151
1,458
zu ermitteln
4,608623
vorgegeben
32
Alternativ: Konditionsmarge auf gebundenes Risikokapital
Statt „gebundenem Kapital“ könnte alternativ das jeweils
„gebundene Risikokapital“ angesetzt werden
Laufzeitverkürzung
Æ VaR des Kredits sinkt
Æ Risikokapital sinkt im Zeitablauf
Zu lösende Aufgabe:
Welche konstante Rendite auf das jeweils gebundene
Risikokapital kann pro Periode aus dem NPV des Geschäfts
ausgeschüttet werden?
33
Auswahl des Refinanzierungszinssatzes
Wie groß ist der Zinsüberschuß des Kreditgeschäftsbereich XYZ?
1. Schichtenbilanzmethode (veraltet)
Ad hoc Annahme: Kredite mit Spareinlagen refinanziert
⇒ Zinsmarge bzw. Konditionenbeitrag = Kreditzins - Sparzins
2. Marktzinsmethode: Separater Konditionenbeitrag für Aktiva und Passiva
Konditionenbeitrag Kredite = Kreditzins - laufzeitkongruenter Refi.-Satz
Konditionenbeitrag Spareinlagen = laufzeitkongr. Refisatz - Sparzins
Fristentransformationsergebnis („Strukturbeitrag“) = Refisatz Kredite - Refisatz
Spareinlagen
⇒ Summe der Beiträge = Kreditzins - Sparzins = Gesamtgewinn
34
Implementierungsansätze der Marktzinsmethode
2. Profit Center müssen sich
fristenkongruent bei ALM refinanzieren
1.
Controlling berechnet
ex post den
kalkulatorischen Erfolg
ALM hält offene Zinsposition
• ALM hat Monopolstellung
• Abbildung über interne Geschäfte
• Alternative: Konkurrenz durch
externe Geschäfte
Problem: Bestimmung fairer Verrechnungspreise!
35
Top-Down Gesamtbanksteuerung unter Nebenbedingungen
Mögliche Zielfunktionen:
RAROC:
R e turn
→ m ax!
xi
V aR
(xi = Geschäftsvolumen
in Produkt i)
Mögliche Nebenbedingungen:
1. Regulatorisches EK
∑ x * Reg.EK − Quote
i
i
≤ EK
i
2. Andere Regulierungen (Großkreditvorschriften etc.)
∑ x (Counterparty y) * EK - Quote ≤ Obergrenze
i
i
3. ...
36
Strategic capital allocation and its work out in the risk
controlling unit
Strategic decisions
target
dividend
risk
appetite
capital
capital
allocation
allocation
investment
opportunities
Risk control tasks
Risk
Risk
limit
limit
allocation
allocation
Risk
Risk
return
return
targets
targets
daily
dailylimit
limit
allocation
allocationand
and
control
control
risk
riskbased
basedpricing
pricing
guidelines
guidelines
37
Risk controlling unit: instruments
Allocation of risk capital / risk limits
Product calculation
• pricing guidelines
• hedge recommendations
• securitization vs. holding on book
Client / product profitability/RORAC calculation
Profit center performance analysis
• RORAC / RAROC calculation
• bonus payments
• expansion / market exit
38
Capital allocation and performance measures - Summary
The state of the art approach for capital allocation is RORAC
RORAC measures expected profit per unit of risk incurred for
generating that profit
RORAC
• can incorporate different types risk
• is universally applicable
Challenges in applying RORAC include
• integrating market, credit, and operational risk
• capturing diversification effects
39

Performance-Messung - Goethe

Transcription

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