Schwerpunkt Finanzen Johann Wolfgang Goethe Universität, Frankfurt (Main) Prof. Dr. Mark Wahrenburg. und Dr. Peter Raupach. Commercial Banking

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1 Schwerpunkt Fnanzen Johann Wolfgang Goethe Unverstät, Frankfurt (an) Prof. Dr. ark Wahrenburg und Dr. Peter Raupach Commercal Bankng Performance easurement & Captal Allocaton 4-stündge Vorlesung mt Übung m SS 2002 Commercal Bankng - Prof. Wahrenburg 1 Purpose and objectves Purpose Understand technques to optmze the rsk-return trade-off of the bank Objectves Understand, how captal allocaton can steer the bank Understand Pros/Cons of dfferent approaches - ROA/ROE - RAROC/RORAC Understand tasks & nstruments of rsk controllng unt Commercal Bankng - Prof. Wahrenburg 2

2 Captal allocaton = Socalsm? The problem s to construct a system of nformaton, accountng, economc ndces and stmul whch permt local decson-makng organs to valuate the advantage of ther decsons from the pont of vew of the whole (frm) [objectve just lke captal allocaton!] The hard thng n a model realzaton s to receve and often to construct necessary data whch n many cases have consderable errors and sometmes are completely absent, snce none needed them prevously. Leond V. Kantorovch, U.S.S.R. Rede Nobelpresverlehung 1975 Commercal Bankng - Prof. Wahrenburg 3 Conflctng objectves RAROC: axmze rsk adjusted return per unt of economc captal Prevent regulatory captal shortage Optmze taxes axmze EPS / RoE Optmze bank ratng, mnmze prob of bank default Keep cash reserves for akqustons Execute strategc bank development plan Commercal Bankng - Prof. Wahrenburg 4

3 Why economc captal? What we generally call profts, the money left to servce equty, s usually not profts at all. Untl a busness returns a proft that s greater than the cost of captal, t operates at a loss. Peter Drucker EVA, Shareholder Value, ROE all are based on a defnton of equty captal employed Wthout an adequate defnton of equty for every busness unt, we cannot dfferentate success/falure from a shareholder perspectve Commercal Bankng - Prof. Wahrenburg 5 Why not use regulatory captal? Too lttle dfferentaton of rsk today AAA-corporates and junk bonds all consume the same regulatory equty! Some busness unts do not requre regulatory equty at all Example: nterest rate rsk takng n the bankng book Rsk percepton of shareholders, not regulators, sets return targets Commercal Bankng - Prof. Wahrenburg 6

4 Objectves of captal allocaton Protecton of the bank Effcent allocaton of resources Rsk based prcng How much captal needed? What busness unts shall expand? How to prce transactons? Commercal Bankng - Prof. Wahrenburg 7 What exactly s the captal to be allocated? Cash Credt Lne Regulatory Captal Economc captal Rsk captal Value at Rsk useless, because s does not restrct volume of dervatves, guarantees etc. stll too often used today can be poor measure of actual rsks all terms have same meanng defnes today s state of art Commercal Bankng - Prof. Wahrenburg 8

5 Evoluton of performance measures Example: calculatng a loan Loan amount 100 Reg. equty 8 Econ. captal 12 Exp. loses 2 % Loan rate 1 0 % Refnance rate 6 % ROA return on assets ROE return on (regulatory) equty RORAC return on economc captal Loan ROA Loan ROE Loan RORAC 100(10% 2% 6%) 100 = 2% 100(10% 2%) 92*6% 8 = 31% 100(10% 2%) 88*6% 12 = 22,6% Commercal Bankng - Prof. Wahrenburg 9 Economc Captal: A unversal concept Probablty of losses confdence level 99% 1% probablty No Loss Reserve expected loss Catastrohe losses Losses captured by economc captal 0% default rate 100% Commercal Bankng - Prof. Wahrenburg 10

6 RORAC s able to encompass all sources of rsk Total VaR Credt VaR arket VaR Operatonal VaR today: smple addng up of VaR numbers future: Integraton of market and credt rsk n order to model dependences Commercal Bankng - Prof. Wahrenburg 11 RORAC s an unversal evaluaton tool on all busness levels Overall Bank RORAC Buness Unt RORAC Clent RORAC Product RORAC Transacton RORAC Commercal Bankng - Prof. Wahrenburg 12

7 RORAC makes performance of all busness unts comparable RORAC Unt Captal Excess Returns RORAC % % % % % % % % % % 10% 20% 30% 40% 50% 60% Value destructon Value creaton Hurdle rate requred by shareholders Commercal Bankng - Prof. Wahrenburg 13 RORAC / RAROC have set today s market standards Ex Ante Analyss: RORAC = Return on Rsk Adjusted Captal RORAC = expected proft economc captal Ex Post Analyss: RAROC = Rsk Adjusted Return on Rsk Adjusted Captal realzed proft - hurdle rate RAROC = economc captal Commercal Bankng - Prof. Wahrenburg 14

8 Do not trust RARAOC alone: some basc problems 1.Dfferentate good luck from superor ablty Is 30% return on a stock portfolo good or bad? Does proft from maturty msmatches n AL demonstrate superor ablty? Is 2% realzed loses on loans wth 3% standard rsk costs outperformance? 2. Allocaton of other costs to busness unts / products How allocate cost of Corporate Center (IT, accountng, Plannng)? How allocate cost of mantanng the branch network? How allocate cost of mantanng a payment system 3. Cross subsdzaton between products Would you close down a credt busness wth bad RAROC, f ths busness s necessary for recevng proftable &A deals? Commercal Bankng - Prof. Wahrenburg 15 A rgorous foundaton of RAROC * K: Buchwert Kredte D: Buchwert Enlagen EK B : arktwert des Egenkaptals EK : Buchwert des Egenkaptals EL : erwartete Ausfallrate (n % des Kredtvolumens) EL: realserte Ausfallrate (n % des Kredtvolumens) RK : Rskokaptal bzw. VaR erwartetes Nettoergebns der Bank = K(r EL) D r f K D E "erwarteter Jahresüberschuss vor Steuern" r : scherer Zns bzw. Refnanzerungszns r :Kredtzns r : Enlagenzns r : Rendte des EK bzw. Egenkaptalkostensatz EKK : Egenkaptalkosten = EK * r E K D * Lt: H. Scherenbeck, Ertragsorentertes Bankmanagement Commercal Bankng - Prof. Wahrenburg 16

9 Performanceanalyse ener rskolosen Bank Re ndteforderung des EK : r Egenkaptalkosten = EKK = EK r Erwartetes Nettoergebns (vor EKK) = K (r EL) D * r f ( ) = K(r EL r ) + D r r + EK *r (Blanzdenttät : K = D + EK ) f K f f D B f K B D Kaptalkosten erwrtschaftet, wenn : Nettoergebns > EKK, bzw : ( ) K(r EL r ) + D r r + EK *r K f f D B f EK = r " Zel ROE der scheren Bank " f Commercal Bankng - Prof. Wahrenburg 17 Ex post Performanceanalyse rskolose Bank ( ) K(r EL r ) + D r r + EK r K f f D B f EK ( ) K(r L r ) + D r r + EK r K f f D B f EK = r " Zel ROE der scheren Bank " f "Realserter ROE" RAROC Realserte Überrendte des EK über de EK-Kosten = Real. ROE - Zel-ROE Commercal Bankng - Prof. Wahrenburg 18

10 Rendteforderung rskante Bank E E, ( ) β ( ) Wertpapermarktlne CAP: r = r + r r = r + r r Defnton Rskokaptal: RK=VaR = ασ EK ( ) ( r r ) EKK = EK r + r r Bank f f E f f E f f β f ρ, = EK rf + RK ασ ( r r ) ρ = r + RK+ ( EK RK) r f, f f ασ E σ ρ σ Zel: EKK als Funkton des RK ausdrücken Zel-RORAC: geforderte Rendte pro Enhet Rskokaptal Commercal Bankng - Prof. Wahrenburg 19 Zahlenbespel EK σ : 20% σ ρ, W ( f) f : 20% :1 : 1 o r r :7% r :5% α :3 20% *1 EKK=1o. 5% + 7% 20% = D RK = 3*20%*1 o. D= D ( r rf)ρ, Zel-RORAC= rf + ασ EKK=RK*RORAC+(EK 7% = 5% + = 16, 6% 3*20% W RK) * r = D *16,6% + (1o 0,6o.) * 5% = D D= D f Commercal Bankng - Prof. Wahrenburg 20

11 Erwrtschaftet Bank hre Egenkaptalkosten? erwartetes Nettoergebns EKK? ( ) K (r EL r ) + D r r + EK * r RK * Zel-RORAC + (EK RK) * r? K f f D B f W f bzw. : ( ) K(r EL r ) + D r r + EK *r (EK RK)*r K f f D B f W f RK Zel-RORAC? Commercal Bankng - Prof. Wahrenburg 21 Anwendung: RAROC ener Kredtbank EK : 1 o. D EK K D f B : 1 o. D K: 10 o. D D: 9 o. D r : 7,5% EL : 1% r : 4,5% r:5% RK: 600 TD Zel-RORAC: 16,6% erwartetes Nettoergebns : 10 o. (7,5%-1%-5%) +9o. (5%-4,5%) + 1 o. *5% = 150 TD + 45 TD + 50 TD = 145 TD 245 TD-(EK RK)rf 225 TD erwarteter RORAC = = = 37, 5% RK 600 TD > Zel RORAC = 16, 6% Re alserte Ausfallrate: 1,5% 195 TD-(EK RK)rf 175 TD Realserter RORAC= = = 29,16% RK 600 TD RAROC = Real. RORAC - Zel-RORAC = 29,16% - 16,6% = 12,5% Commercal Bankng - Prof. Wahrenburg 22

12 Concluson We must dfferentate 3 rsk adjusted return concepts: Target-RORAC hurdle rate that must be earned n order to earn cost of equty depends on: - cost of equty (beta factor of bank wthn CAP) - dfference between market value of equty and economc captal Expected RORAC calculated wth expected losses Realszed RAROC calculated wth realzed loses Commercal Bankng - Prof. Wahrenburg 23 Bottom Up estmaton of economc captal x OUTSTANDINGS ($000) Rsk Remanng Tenor (Years) Grade Demand Total 1 (1,697) (20,193) 2,659 2,535 (16,698) ,830 16, , , , ,557 25,025 6, ,521 4, ,906 4 (675) 479,472 28,782 19,192 1,969 3, , ,334 4, , , , , , , , , NA ,006 22,487 (110,271) 15,380 2,960 19,371 3,820 8,675 3,605 29, ,961 Total 2,224 1,888,901 97,699 -$ 81,660 22, ,482 23,516 3,820 10,927 3,605 29,883 2,201,679 $ $ $ $ $ $ $ $ $ $ $ CAPITAL FACTORS (bps) Rsk Remanng Tenor (Years) Grade Demand ,000 1,050 1,050 1,050 1,050 1, ,000 1,000 1,000 1,000 1,000 1,000 1,000 1,000 1,000 1,000 1, ,900 1,900 1,900 1,900 1,900 1,900 1,900 1,900 1,900 1,900 1, ,300 3,300 3,300 3,300 3,300 3,300 3,300 3,300 3,300 3,300 3, ,500 4,500 4,500 4,500 4,500 4,500 4,500 4,500 4,500 4,500 4,500 NA = REQUIRED CAPITAL for OUTSTANDINGS ($000) Rsk Remanng Tenor (Years) Grade Demand Total 1 (2) (25) (12) , ,367 4 (12) 8, , , , , , , , , NA 5 5, (4,847) , ,523 7,151 Total ,590 2,127 4, ,795 1, ,542 50,314 $ $ $ -$ $ $ $ $ $ $ $ $ Commercal Bankng - Prof. Wahrenburg 24

13 Qute often, due to data avalablty problems, economc captal s estmated as a functon of expected loss Typcal Captal as a Functon of Expected Annual Loss n Consumer (Bass Ponts) 1,200 1, ,000 1,500 2,000 2,500 3,000 3,500 4,000 4,500 5,000 Expected Loss Commercal Bankng - Prof. Wahrenburg 25 CAP vs. RAROC perspectve CAP Cost of equty accordng to CAP RAROC target return on economc captal r = r + ( r r ) ß f f VaR = α * PV * σ r f Rsk, measured by ß : σ σ, 2 σ What rsk contrbuton to dversfed portfolo? What contrbuton to probablty of extreme losses / of default? Commercal Bankng - Prof. Wahrenburg 26

14 RAROC s closely related to Sharpe Raton Sharpe Rato E(R) CAP Captal market lne R = r F + (r r F) σ σ R r Sharpe Rato = F σ σ Glt nach CAP nur für effzente Portfolos! Commercal Bankng - Prof. Wahrenburg 27 However, CAP tells us that sngle postons should be evaluated by securty market lne E(R) Proft Center 1 } Jensens α CAP Securty market lne Proft Center 2 R = r F + ( r r F ) β r F ß Commercal Bankng - Prof. Wahrenburg 28

15 Is RAROC consstent wth CAP? Example: An asset has a CAP-beta of 0 expected return (hurdle rate) accordng to CAP = r f RAROC: Compensaton for economc captal requred, f poston affects bank VaR requred return > equlbrum return n captal market A trader who beats the market does not neccessarly produce a postve RAROC Commercal Bankng - Prof. Wahrenburg 29 RAROC wth solated VaR vs. contrbuton to total bank VaR RAROC 1 = Re turn VaR der Poston Each busness unt optmzes own rsk poston only RAROC 2 = Re turn VaR Betrag der Poston accounts for correlaton wth other busness unts Incentve to optmze total bank portfolo Commercal Bankng - Prof. Wahrenburg 30

16 Perodenzurechnung des Ergebnsses aus Kredtgeschäft Bespel: Endfällger rskoloser Kredt Kondtonenbetragsbarwert = = NPV des Kredts Abznsung mt laufzetkongruenten Zeroznssätzen Zns Zns Zns ( 100 -Dsago) T 1+ r1 (1+ r2 ) (1+ rt ) Interpretaton a): NPV kann n t 0 als Dvdende entnommen werden Interpretaton b): NPV kann als Dvdendenstrom entnommen werden. we hoch st de Dvdende pro Perode? Commercal Bankng - Prof. Wahrenburg 31 Perodenzurechnung des Kondtonenbetragsbarwert Alternatve a) Welche Annutät kann aus NPV gezahlt werden? Alternatve b) Welche Rendte des (jewels) gebundenen Kaptals kann aus NPV pro Perode gezahlt werden? (KBBW) 1 k = 1 gebundenes Kaptal n t = Nomnalwert Tlgung k Bespel zur Verrentung der Kondtonsmarge Zetpunkt (1) Gebundenes Kaptal (2) Kondtonsmarge 3,34% 3,34% (3) Rente (1)*(2) 3,34 1,67 (4) Abznsungsfaktoren 0,943 0,873 (5) Barwerte (3)*(4) 3,151 1,458 (6) KB-Barwert (Summe(5)) 4, zu ermtteln vorgegeben Commercal Bankng - Prof. Wahrenburg 32

17 Alternatv: Kondtonsmarge auf gebundenes Rskokaptal Statt gebundenem Kaptal könnte alternatv das jewels gebundene Rskokaptal angesetzt werden Laufzetverkürzung VaR des Kredts snkt Rskokaptal snkt m Zetablauf Zu lösende Aufgabe: Welche konstante Rendte auf das jewels gebundene Rskokaptal kann pro Perode aus dem NPV des Geschäfts ausgeschüttet werden? Commercal Bankng - Prof. Wahrenburg 33 Auswahl des Refnanzerungsznssatzes We groß st der Znsüberschuß des Kredtgeschäftsberech XYZ? 1. Schchtenblanzmethode (veraltet) Ad hoc Annahme: Kredte mt Sparenlagen refnanzert Znsmarge bzw. Kondtonenbetrag = Kredtzns - Sparzns 2. arktznsmethode: Separater Kondtonenbetrag für Aktva und Passva Kondtonenbetrag Kredte = Kredtzns - laufzetkongruenter Ref.-Satz Kondtonenbetrag Sparenlagen = laufzetkongr. Refsatz - Sparzns Frstentransformatonsergebns ( Strukturbetrag ) = Refsatz Kredte - Refsatz Sparenlagen Summe der Beträge = Kredtzns - Sparzns = Gesamtgewnn Commercal Bankng - Prof. Wahrenburg 34

18 Implementerungsansätze der arktznsmethode 1. Controllng berechnet ex post den kalkulatorschen Erfolg 2. Proft Center müssen sch frstenkongruent be AL refnanzeren AL hält offene Znsposton AL hat onopolstellung Abbldung über nterne Geschäfte Alternatve: Konkurrenz durch externe Geschäfte Problem: Bestmmung farer Verrechnungsprese! Commercal Bankng - Prof. Wahrenburg 35 Top-Down Gesamtbanksteuerung unter Nebenbedngungen öglche Zelfunktonen: RAROC: Return V ar max! x (x = Geschäftsvolumen n Produkt ) öglche Nebenbedngungen: 1. Regulatorsches EK x * Reg.EK Quote 2. Andere Regulerungen (Großkredtvorschrften etc.) x EK (Counterparty y)* EK - Quote Obergrenze Commercal Bankng - Prof. Wahrenburg 36

19 Strategc captal allocaton and ts work out n the rsk controllng unt Strategc decsons Rsk control tasks target dvdend rsk appette nvestment opportuntes captal captal allocaton allocaton Rsk Rsk lmt lmt allocaton allocaton Rsk Rsk return return targets targets daly dalylmt lmt allocaton allocatonand and control control rsk rskbased basedprcng gudelnes gudelnes Commercal Bankng - Prof. Wahrenburg 37 Rsk controllng unt: nstruments Allocaton of rsk captal / rsk lmts Product calculaton prcng gudelnes hedge recommendatons securtzaton vs. holdng on book Clent / product proftablty/rorac calculaton Proft center performance analyss RORAC / RAROC calculaton bonus payments expanson / market ext Commercal Bankng - Prof. Wahrenburg 38

20 Captal allocaton and performance measures - Summary The state of the art approach for captal allocaton s RORAC RORAC measures expected proft per unt of rsk ncurred for generatng that proft RORAC can ncorporate dfferent types rsk s unversally applcable Challenges n applyng RORAC nclude ntegratng market, credt, and operatonal rsk capturng dversfcaton effects Commercal Bankng - Prof. Wahrenburg 39