Integrating credit and interest rate risk: A theoretical framework and an application to banks' balance sheets

Transcription

1 Inegrang cred and neres rae rsk: A heorecal framework and an applcaon o banks' balance shees Mahas Drehmann* Seffen Sorensen** Marco Srnga*** Frs draf: Aprl 26 Ths draf: June 26 Cred and neres rae rsk n he bankng book are he wo mos mporan rsks faced by commercal banks. In hs paper we derve a conssen and general framework o measure he rskness of a bank whch s subjec o correlaed neres rae and cred rsk. The framework accouns for all sources of cred rsk, neres rae rsk and her combned mpac. As we model he whole balance shee of a bank he framework no only enables us o assess he mpac of cred and neres rae rsk on he bank s economc value bu also on s fuure earnngs and capal adequacy. We apply our framework o a hypohecal bank n normal and sressed condons. The smulaon hghlghs ha s fundamenal o measure he mpac of correlaed neres rae and cred rsk jonly as well as on he whole porfolo of banks, ncludng asses, lables and offbalance shee ems. Key words: Inegraon of cred rsk and neres rae rsk, asse and lably managemen of banks, economc value, sress esng JEL classfcaon: G21; E47; C13 * Sysemc Rsk Assessmen Dvson, Bank of England, Threadneedle Sree, London, EC2R 8AH. E-mal: mahas.drehmann@bankofengland.co.uk ** Sysemc Rsk Assessmen Dvson, Bank of England, Threadneedle Sree, London, EC2R 8AH. E-mal: seffen.sorensen@bankofengland.co.uk *** Sysemc Rsk Assessmen, Bank of England, Threadneedle Sree, London, EC2R 8AH. E-mal: marco.srnga@bankofengland.co.uk. Correspondng auhor. The vews and analyss expressed n hs paper are hose of he auhor and do no necessarly reflec hose of he Bank of England or he Moneary Polcy Commee members. We would lke o hank Ma Corder and Chrs Kubelec for provdng us wh he mpac of he sress scenaro on PDs and rsk-free yeld curves and Greg Dudley-Smh for excellen research asssance. We would also lke o hank Prasanna Ga, Andy Haldane and he parcpans of a Bank of England and a Bank of Ausra s (OeNB) semnar for her useful commens. As usual, all remanng errors are ours.

2 1 Inroducon Cred and neres rae rsk are he wo mos mporan rsks faced by commercal banks. Bu as Jarrow and Turnbull (2) pon ou economc heory ells us ha marke and cred rsk are nrnscally relaed o each oher and no separable. In hs paper we concenrae on he major source of marke rsk for commercal banks: neres rae rsk n he bankng book. Frs, we derve a general framework o measure he rskness of banks whch are subjec o correlaed neres rae and cred shocks 1. In lne wh he curren leraure hs framework ncorporaes he negraed mpac of neres rae and he cred rsk on banks asses. Bu, we show ha s mporan o model he whole porfolo of a bank: asses, lables and off-balance shee ems. Ths no only enables us o assess he mpac of cred and neres rae rsk on rsk adjused dscoun raes and, hence, banks' economc value bu also on fuure expeced profs and capal adequacy over me. In he second par of he paper, we apply he framework o look a he rskness of a hypohecal bank n a severe sress scenaro. We show ha s fundamenal o measure he mpac of correlaed neres and cred rsk jonly and on he whole porfolo of banks, ncludng asses, lables and off-balance shee ems. When seng capal or prcng asses he focus s generally on defaul rsk only. For example, he Meron (1974) model uses he nsghs from opon prcng o derve he lkelhood ha he value of asses fall below he defaul hreshold and he frm defauls. Smlarly, reduced form models n he spr of Jarrow and Turnbull (1996) only model he defaul nensy. Basel II and commercal cred porfolo models such as Moody s KMV or CredRsk + also accoun for defaul rsk only 2. A broader defnon of cred rsk ncludes changes n he value of ne asses due o changes n cred spreads, downgrades as well as defauls. And all hese facors are mporan when assessng he mpac of cred rsk on he economc value and profably of a porfolo. Ineres rae rsk s also a broad erm and may be arbuable o reprcng msmaches of asses, lables and off-balance shee ne posons, ncludng bass and yeld curve rsk 3. For hs reason s mporan o have a flexble framework o capure he sensvy of economc value and ne neres ncome o changes n he level and slope of he erm srucure of he rsk-free neres rae as well as he neracons of neres rae and cred rsk. Gven he complexy of he underlyng sources of neres rae rsk emprcal papers fnd hard o suppor s mporance for banks rskness. Followng Flannery and James (1984) several papers fnd a srong negave mpac of neres raes on bank sock reurns (for a recen sudy see Fraser e a 22). However, Chen and Chan (1989) argue ha hs s hghly dependen on he acual sample perod. A BIS sudy by Englsh (22) also concludes ha seems unlkely ha neres rae changes are an mporan facor for he sably of a bankng sysem, even hough Englsh acknowledges ha neres rae rsk may be an mporan source of volaly of profs. Englsh suppors hs conclusons by an economerc analyss of annual aggregae ne neres ncome n dfferen counres. He only fnds weak suppor ha changes n he slope of he yeld curve as well as long- and shor-erm neres raes mpac on ne neres ncome. In a recen sudy on neres rae rsk n he Belgan 1 By correlaed cred and neres rae rsk we do no necessarly mply a lnear relaonshp bu ha we model he wo rsks dependence. 2 Unforunaely, hese models also assume non-sochasc neres raes and herefore canno assess he mporance of neres rae rsk on cred exposures. 3 Ineres rae rsk also arses from dfferences n embedded opons of asses and lables. Even hough he framework could be exended o capure oponales we do no consder hem n hs paper. 2

3 bankng secor, Maes (25) argues ha neres rae rsk s mporan for bankng sably, bu agan only fnds weak emprcal evdence when lookng a ne neres ncome. Banks are aware of he mporance of neres rae rsk and measure her exposure regularly. They do so by underakng sensvy ess of parallel shfs or wss n he rsk-free yeld curve. One of he smples sensvy ess ofen underaken s gap analyss, where banks or regulaors assess neres rae rsk by purely lookng a he ne reprcng msmach beween asses, lables and off-balance shee ems 4. Such ess mplcly assume ha shocks o he rsk-free yeld curve have no mpac on he cred qualy of asses. However, as poned ou already, neres raes rsk and cred rsk are correlaed and we show ha gnorng he mpac of neres rae rsk on cred rsk can lead o a severe underesmaon of rsk. We wll also show why annual ne neres ncome may be oo aggregaed o dsenangle he complex effecs of neres raes on banks rskness. Followng an neres rae ncrease profably nally falls due o a rse n wre offs and a decrease n ne neres ncome as margns beween shor erm borrowng and long erm lendng are compressed. However, as he bank gradually reprces s asses, ne neres ncome sars o ncrease because passes he hgher cred rsk and neres raes o s borrowers. Over me he second effec ouweghs he frs unl he nal level of profably s recovered. Gven hese opposng effecs and combned wh oher flucuaons n he daa s no surprsng ha an economerc analyss of ne neres ncome usng annual daa fnds hard o suppor he mporance of neres rae rsk for banks. Jarrow and Turnbull (2) are among he frs o show heorecally how o negrae neres rae (among oher marke rsks) and cred rsk n a reduced form model. Ther nsghs are backed by srong emprcal evdence ha neres rae changes mpacs on he cred qualy of asses. For example, Jarrow and van Devener (1998) show ha n erms of hedgng a bond porfolo, boh cred and neres rae rsk have o be aken no accoun. Grundke (25) fnds ha sgnfcan errors are made when he correlaed naure of rang ransons, cred spreads, neres raes and recoveres s gnored. Smlarly, neres raes have been denfed as he key rsk drver of aggregae cred qualy n he UK (e.g. see Beno e al, 21, and Whley e al, 24) All hese papers look a he negraed mpac of cred and neres rae rsk on asses only, by for example modellng a bond porfolo. However, hey do no assess he mpac of neres and cred rsk on lables or off-balance shee ems. In a seres of papers, Barnhll and varous co-auhors (2, 21 and 24) aemp o measure cred and marke rsk for he whole porfolo of banks. They develop a smulaon framework o revalue asse and lables dependng on he sae of several sysemac rsk facors, such as he erm srucure of rsk-free and rsky neres raes, sock ndces and propery prces. They negrae neres rae and cred rsk for corporaes by smulang he equy o deb rao condonal on sysemac rsk facors and hen map no dfferen rang classes or defauls. Smlarly, for loans o ndvduals hey smulae he loan o value (LTV) rao condonal on sysemac rsk facors and assume ha a borrower defauls f he LTV s below a ceran hreshold. All oher asses and lables are valued a he condonal rsk-free neres rae. 4 Generally, gap analyss allocaes asses, lables and off-balance shee ems o me buckes accordng o her reprcng characerscs and calculaes her ne dfference for each bucke. Because of hs neng procedure, gap analyss may fal consder non-lneares and, consequenly, underesmae he mpac of neres rae rsk. For example, some shor-erm cusomer depos raes rack he rsk-free rae plus a negave spread. Hence, for large falls n he rskfree erm srucure, banks may no be able o lower depos raes n lne wh he rsk-free rae because bounded by zero. By modellng he whole porfolo we can capure hs compresson n banks ne margns. 3

4 To assess he sably of a bank or bankng sysem, hey focus on he dsrbuon of he economc value of banks,.e. he marke value of asses mnus lables. They fnd ha cred rsk s he mos sgnfcan rsk facor for banks. Bu her concluson s lkely o be msleadng as hey gnore one of he mos mporan sources of neres rae rsk - reprcng msmaches beween asses and lables 5. In conras o Barnhll e al and mos of he leraure we no only look a economc value bu also a fuure earnngs and capal raos. Volaly of earnngs s an mporan focal pon for banks because severe falls n profs can pose a hrea o banks capal and may creae lqudy problems, eher due o a lack of cash or o a downgrade whch may lead o fundng problems. The measuremen of banks economc value, however, provdes a more comprehensve vew of he poenal long-erm exposure o cred and neres rae rsk. Some of he few papers whch do ake boh an economc value and an earnngs perspecve are Jobs and Zenos (23) and Jobs e al (23, 26). These papers look a opmal porfolo selecon n he conex of dynamc asse and lably managemen. They smulae correlaed neres raes and cred spreads as well as defauls for a porfolo of corporae bonds and rack fuure porfolo valuaons, ncorporang all coupon paymens. Usng hs nformaon hey compue he opmal porfolo allocaon f here s only one nvesmen decson ex-ane or f he porfolo can be rebalanced a each pon n me. We canno use cred spreads from bond daa as we look a banks porfolos whch conan a wde range of non-raded asses and lables. Insead, we model corporae and household cred rsk drecly. Furher, and more mporanly, we model he complex cash flows from lables wh dfferen maures raher han assumng a smple cash accoun as Jobs and hs co-auhors do. Our approach also akes accoun of neres rae sensve off-balance shee ems. The heorecal se-up of our paper s kep very general. In he emprcal par we buld on a macro sress esng model as descrbed n Bunn e al (25). Ths model sars wh he general assumpon ha condonal on sysemac rsk facors corporae and household secor defauls are ndependen. And denfes macroeconomc facors as he key drvers for cred rsk. We combne our cred rsk model wh a dynamc yeld curve model lnkng he rsk-free yeld curve o developmens n macro facors (Debold e al, 26). By lnkng cred rsk and he rsk-free yeld curve o he same sysemac rsk facors we are able o capure he underlyng correlaon beween cred and neres rae rsk. Ths allows us o assess he mpac of cred and neres rae rsk on rsk adjused dscoun facors whch ake accoun of shfs n he rsk-free yeld curve as well as he defaul nensy of borrowers. Expandng he sngle asse framework of Duffe and Sngleon (23) o a porfolo of asses and lables we can herefore compue he economc value of banks whch are subjec o cred and neres rae rsk. Bu he framework also allows us o projec expeced profs n fuure perods. In parcular, we are able o calculae expeced wre-offs and expeced ne neres ncome, he laer by explcly modellng he reprcng of asses and lables. Hence, we are also able o assess expeced earnngs, profably as well as capal raos condonal on he crysallsaon of cred and neres rae rsk. In he smulaon we apply our framework o a hypohecal bank whch s subjec o a combnaon of sress es scenaros smlar o hose developed for he IMF Fnancal Sably Assessmen 5 The papers also look a a maury msmach of +/- one year and conclude ha s mporan. Bu +/- one year s clearly oo smplsc o capure he full mpac of he maury mss-mach on he rskness of banks. 4

5 Programme of he UK n Even hough he sably of he bank s no hreaened n he sress scenaro, we fnd srong evdence ha neres rae and cred rsk have o be assessed smulaneously as well as jonly for asses and lables. In lne wh Bunn e al (25) we show ha wre-offs ncrease sgnfcanly afer he sress. As we also model ne neres ncome we are able o llusrae ha he addonal margn compresson decreases profs even furher n he frs few quarers. Bu losses are gradually offse once he bank sars o reprce asses and margns reflec he change n he rsk-free yeld curve and cred qualy agan. The offseng effec of hgher ne neres ncome mples ha afer hree years profs are roughly a he same level as n he baselne scenaro, even hough wre-offs peak only n he hrd year and are sgnfcanly hgher han n he baselne scenaro. The emprcal exercse hghlghs wo mporan nnovaons of our framework. Frs, n conras o sandard sress esng models 7 we are able o assess boh he economc value as well as he profle of he man componens of profs durng bengn and sressed condons. Second, we can decompose he change n ne profs no changes drven by cred rsk, neres rae rsk as well as correlaed cred and neres rae rsk. Usng our new approach, we show ha gnorng he correlaons beween neres rae and cred rsk as well as only modellng he asse sde of a bank does severely dsor he rsks faced by banks. The remander of he paper s srucured as follows. In Secon 2 we dscuss our new general framework o negrae cred and neres rae rsk n he bankng book. In Secon 3 we dscuss he modellng of he erm-srucure of neres rae of dfferen asses and lably classes. In Secon 4 we presen he resuls of he sress es and n Secon 5 we nvesgae wheher neres rae, cred or he neracon beween boh rsks s he key rsk drver. Our resuls are evaluaed agans a number of sensvy ess n Secon 6. Fnally, we summarse he man conclusons of he paper n Secon 7. 2 The framework Ths secon sars by dscussng he negraon of neres rae and cred rsk for a generc asse and hen looks a a bank as a porfolo of several asses and lables wh dfferen rsk and reprcng characerscs. 2.1 A generc asse The economc value of a generc asse s smply he rsk-adjused dscouned value of fuure coupon paymens and he prncpal. For smplcy we assume ha all asses are equvalen o bulle bonds.e. repay he prncpal only a maury. For example, such an asse could be a fxed-neres rae bond wh no embedded opons or a smple varable rae bank loan. Gven he nformaon se avalable a me, he economc value of asse wh maury T s: T EVA = D + kc A + D + T k= 1 A (1) 6 For a deal descrpon of he nal IMF sress ess see Hoggarh and Whley (23). 7 For an overvew of sress esng models see Sorge (25). 5

6 where A s he prncpal and s he consan coupon rae for he generc asse deermned a =. C The dscoun funcon s gven by: + k = k D d where he perod by perod dscoun raes s: E ( R, + d l= + l ; + l 1 (2) 1 = (3) 1+ E ( R ) + l 1; + l + l 1; + l + l 1 l ) s he me expeced rsk adjused nomnal neres rae pad by he generc asse beween +l-1 and +l. To smplfy noaon, we assume ha = for he remander of hs secon. Absracng from he lqudy premum, ( R l 1, l and a rsky componen relaed o he cred rsk of he asse: E ) can be decomposed no a rsk-free componen E ( Rl 1; l ) = E ( rl 1; l ) + E ( s l-1;l ) (4) where E ( sl-1;l ) = E ( λ l-1;l LGDl ) s he cred rsk premum, E ) he expeced shor rae ( r l 1; l beween l-1 and l, LGD l he expeced loss gven defaul for borrower a l and λ l 1;l he expeced defaul nensy of borrower beween l-1 and l, condonal on survval up o l-1. All expecaons are aken subjec o he nformaon se a me. Ths decomposon holds n connuous me only. In dscree me Duffe and Sngleon (23) 8 show ha he expeced rsk adjused neres rae beween l and l+1 can be calculaed as: where l 1 l E ( rl 1; l ) + E ( PDl 1; l LGDl ) E ( Rl 1; l ) = (5) 1 E ( PD LGD ) l 1; l l PD ; s he probably of defaul of borrower beween l-1 and l condonal on survvng unl l-1. Agan, all expecaons are aken subjec o he nformaon se a me =. Arbrage wll ensure ha a he me of ssuance (=) he economc value equals he face value of he asse. Ths mples ha EVA = = n equaon (1). Solvng for C = we oban: C 1 D = T k= 1 D T k (6) Equaons (5) and (6) are crucal for undersandng he channels hrough whch cred and neres rae rsk are correlaed. Frs, boh he expeced rsk premum and he expeced rsk free yeld curve are dependen on a common se of macroeconomc rsk facors. Hence, unexpeced changes n hese 8 The above formula holds for coupon bonds f he same LGD apples o boh coupons and prncpal. 6

7 rsk facors do mpac boh cred and neres rae rsk. Second, unexpeced movemens n he rskfree yeld curve do change borrowers cred rsk 9. When economc condons change over me, he expeced yeld curve, he expeced PDs and LGDs of he asse wll adjus nsananeously. The dscoun facors, D + k, wll herefore also adjus mmedaely. As coupon raes reman fxed he economc value of an asse wll dverge from s face value. However, once he asse can be reprced coupon paymens wll reflec he new economc condons and he asse's economc value wll equal s face value agan. For a bank hs mples ha whs he economc value always reflecs nsananeously all fuure and curren economc condons, neres ncome wll adjus parally as s asses and lables gradually reprce. 2.2 The generc bank A bank can be seen as a large porfolo of asses and lables 1. In parcular, we wll look a N asse classes A and M lably classes L j. where all exposures n an asse (lably) class (j) have he same rsk characerscs. Whn each class ndvdual exposures may have dfferen reprcng buckes bu we assume for smplcy ha he maury of an asse (lably) concdes wh s reprcng characerscs. Accordng o he reprcng and rsk characerscs each asse s prced accordng o formulae 1-5. In heory hese formulae also apply o all lables usng he bank s own PD and LGD. Bu as we wll dscuss shorly we wll need o rea lables dfferenly o mach emprcal observaons. To assess he vulnerably of a bank o cred and neres rae rsk, we adop boh an economc value and an earnngs perspecve. As dscussed earler, volaly of earnngs s an mporan focal pon for he sably of a bank n he shor run because a fall n ncome and an ncrease n wre-offs can pose a hrea o banks capal and possbly lqudy. The measuremen of he mpac of a shock on a bank s economc value provdes a more comprehensve vew of he poenal long-erm exposures o cred and neres rae rsk. Clearly, he earnngs and economc value perspecves are relaed as he economc value of a bank should be equvalen o he dscouned sum of all fuure earnngs n a rsk neural world. Before connung wh he heorecal se-up we need o clarfy he noaon. To enhance readably for a mul-asse and mul-lably bank we drop he expecaon operaor and wll do so for he remander of he paper. Bu he reader should keep n mnd ha all calculaons are based on expecaons condonal on he nformaon se avalable a he me of prcng. We wll also use subscrp o ndcae he flow beween -1 and. To clarfy: for sock varables, for example he economc value of a loan, he subscrp ndcaes he value of he varable a me. Whle for flow varables, for example a bank s neres recevables, he subscrp ndcaes he accrued value of he varable beween -1 and. 9 There s also a feedback from cred rsk o neres raes. Such effec s parally embedded n he macro-model, whch we use o smulae he sysemac rsk facors. Bu hs channel s hard o quanfy formally and we, herefore, do no explcly consder n hs paper. 1 More generally, a bank s porfolo also ncludes off-balance shee ems. In he framework we do no dsngush wheher asses and lables are on- or off-balance shee ems. Bu we wll model hem separaely n our applcaon n he nex secon. 7

8 2.2.1 The economc value perspecve A frm s economc value EVB s he economc value of s asses (EVA) mnus he economc value of s lables (EVL): EVB = EVA EVL wh EVA = N = 1 EV A and EVL = M j= 1 EVL j (7) A key ssue n he reamen of banks lables s he modellng of he banks own cred rsk. One could argue ha lables should be dscouned usng he rsk-free rae and a bank s PD and LGD. Whle hs seems o be he case for banks subordnaed lables, s well known ha shorer-erm cusomer depos raes are generally below he rsk-free neres rae even when accounng for nonneres coss ne of fees (see for example Maes, 25). Ths may be he resul of depos nsurance schemes or barrers o enry lmng compeon. Furhermore, as a bank s cred condons deerorae s PD ncreases and, ceers parbus, he economc value of s deposs decreases. Hence, a deeroraon n asse qualy wll no be fully refleced n he ne economc value of he bank. In some exreme cases he fall n EVL can more han offse ha n EVA wh he ne resul of an ncrease n he bank s economc value 11. Alhough hs may be welcomed by shareholders, s n enson wh he concern of deposors, debholders and regulaors abou he ably of banks o repay lables a par when due. Gven ha our concern s o measures banks fnancal srengh from he perspecve of he overall sably of he fnancal sysem, we are neresed n banks ably o repay all her lables a par when due. Hence, our frs condon o assess he sably of a bank s o see wheher he economc value of asses condonal on cred and neres rae rsk s greaer han he face value of all s lables M FVL = L. Therefore, he economc value perspecve s: j= 1 Condon 1 Economc Value: EVA > FVL (8) From a regulaory perspecve hs condon has wo benefs. Frs, provdes a long erm vew of he bank s ably o repay all s lables when due. Second, n severe sressng condons wh hkes n neres raes, s lkely o represen an upper bound n comparson o an economc-value analyss as he face value wll be greaer han he economc-value of lables The earnngs perspecve Whereas he economc value perspecve provdes a long erm vew based on economc fundamenals, he earnngs perspecve focuses on wheher a bank would be suffcenly well 11 For example, consder a bank wh a posve ne value whch has o wre-off 1 per cen of s asses due o a sudden dosyncrac adverse shock. And assume ha he shock nearly wpes ou he bank s capal. As a consequence, he bank s PD s lkely o ncrease dramacally, say from.1 o.5. If he bank has lables wh an average maury of one year (and r and LGD are assumed o be consan a 5% and 5% respecvely) such an ncrease would decrease EVL of lables by around 19%; well above he 1% loss on he asse sde. The ne resul would be an ncrease n he bank s economc value. 8

9 capalsed n all fuure saes of he world. Ths s an mporan dfference as a parcular pah of profs may well lead a bank o be undercapalsed n specfc perods even hough Condon 1 s sasfed. Ths may occur f a bank ncurs severe losses n he shor run whch are ouweghed by suffcen profs n fuure perods. From an economc value perspecve hs bank would be solven bu because of marke or regulaory consrans may fnd dffcul o connue o operae. For example, a bank wh a capal adequacy rao below he mnmum requremen could be prone o lqudy runs. I s herefore mporan o assess wheher a bank s expeced capal adequacy gven he expeced fuure pah of earnngs remans above he regulaory mnmum k for all perods n he medum erm W 12. Hence our second condon s: Condon 2 Capal adequacy SF RWA > k W (9) < where RWA denoes expeced rsk weghed asses and SF expeced shareholder funds, whch are assumed o be he only capal of he bank. Rsk weghed asses are calculaed under wo dfferen approaches. We frs ake rsk weghs o be consan over me:.5 for ner-bank lendng,.35 for morgage lendng,.75 for unsecured lendng and 1 for corporae loans n our smulaon. Ths could be seen as an approxmaon of Basel I framework currenly n use. Under hs approach, rsk weghed asses are smply he weghed sum of exposures o asse a me wh rsk weghs w dfferng across asse classes. Hence Condon 2 under hs approach s: Condon 2a Capal adequacy - consan rsk weghs SF RWA CRW > k < W wh RWA As we are especally neresed n severe manfesaons of cred rsk, he consan-rsk-wegh approach descrbed above may no be suable as may underesmae he rsks o he capal adequacy of he bank. We herefore also use he Basel II nernal rang based approach whch w accouns for me-varyng rsk-weghs for dfferen asse classes (see Bank for Inernaonal Selemens, 24). Hence Condon 2 under hs approach becomes: Condon 2b Capal - nernal rang based approach CRW = w A (1) SF RWA IRB > k < W wh RWA IRB = w A (11) 12 We wll only look a Ter 1 capal (proxed by shareholder funds) n our smulaon for whch he curren mnmum capal requremen relave o rsk weghed asses s 4%. And we wll consder hree years as he medum horzon W. 9

10 2.2.3 Assessng shareholder funds and fuure cash flows Smulang expeced shareholder funds SF nvolves rackng expeced ne profs whch eher grow by reaned earnngs (.e. profs afer axes and dvdend payous) or decrease by losses n whch case no axes and dvdends are pad 13. Hence, shareholder fund can be compued as SF θ (12) = max( ; NP ) + mn(; NP ) + SF 1 wh θ<1 gven ha he bank pays axes as well as dvdends. For a represenave bank, expeced ne profs (NP ) beween perod -1 and are he sum of expeced ne neres ncome plus expeced oher ncome (OI ) mnus expeced wre-offs (WR ) and expeced coss (Cos ). Expeced ne neres ncome n urn s he sum of he expeced oal cash flows he bank receves from s asses (CFA ), mnus expeced oal cash flows has o pay on s lables CFL. NP = ( CFA CFL ) WR + OI Cos (13) For smplcy we assume ha oher ncome and coss are drven by a consan exogenous process calbraed o hsorcal daa for an average UK bank. Our approach hus concenraes on smulang expeced wre-offs and expeced ne neres ncome, generally he man source of ncome for commercal banks. The conrbuon of a sngle asse o ne neres ncome s smple o calculae: n he case of no defaul he conrbuon s C A, - whle f he borrower defauls he conrbuon s ( 1 LGD ) C A 1. Furhermore, n he perod of defaul he bank wll wre off s losses: LGD A 1. Hence, he expeced conrbuon o ne neres ncome one perod ahead s: CFA = [( 1 PD ) + PD (1 LGD )] C A 1 and expeced wre-offs are WR = PD LGD A 1. In hs secon, we assume ha LGDs are no me dependen. Even f concepually he same, dervng CFA for a porfolo can become compuaonally very demandng as all N asses classes have dfferen PDs and LGDs as well as dfferen reprcng buckes b. In addon, we wan o assess expeced cash flows no only one perod ahead bu no he medum erm W. Therefore, we have o make an assumpon on he (re-)nvesmen behavour of banks afer he asses maure. To keep our base lne smulaon as smple as possble we assume ha ndependen of he nal maury or PD bucke all borrowers have connung fnancng needs. Therefore, unless here s a defaul every borrower wll roll over her loan wh he same maury bucke as before or, equvalenly, he bank connues o nves no new projecs wh he same reprcng and rsk characerscs as he maured asses. Ths mples ha he bank s porfolo composon changes only n lne wh defauled asses. 13 Ths equaon mplcly assumes ha he bank pays dvdends proporonally o s ncome and ha he bank s payng dvdends as long as s able o do so. Furhermore, s assumed ha losses canno be carred forward o offse fuure axes. However, s easy o ncorporae dfferen ax and dvdend regmes n our smulaon as we wll show n our sensvy analyss. 1

11 Gven he behavoural assumpon, he expeced evoluon of each asse class adjusng for defaul s: A = A 1 (1 PD LGD ) and A = and he oal expeced cash flow beween -1 and s: CFA = N = 1 b= + T 1 b= 1 C, b 1 l= 1 I A l, b 1 C [(1 PD ) + PD (1 LGD )], b l A, b 1 [(1 PD ) + PD (1 LGD )] A + (14) (15) wh I l =1 n perod l when asses n bucke b have been reprced he las me pror o I l = oherwse The nerpreaon of equaon (15) s relavely sraghforward. The frs par n he bg brackes sums he expeced coupon paymens asse classes whch have no been reprced a me and he second par sums expeced coupon paymens of asse classes whch have been reprced he las me n perod l pror o me. In order o ensure conssency wh equaon (5) we assume ha n case of defaul he coupon n ha perod can be parally recovered. Ths s shown n equaon (15) by means of he wo LGD erms. Fnally, equaon 15 sums over he N dfferen asse classes. Gven he evoluon of expeced asses, expeced fuure wre-offs are gven by: WR = N = 1 LGD PD A 1 (16) Equaon (15) and (16) hghlgh how profs are drven by changes n wre-offs, exposures and cash flows conrbuons o ne neres ncome. For example, f economc condons deerorae expeced wre-offs wll ncrease. Such an ncrease wll also decreases and n urn CFA colleced beween me -1 and, ulmaely reducng NP. On he oher hand, he bank also receves hgher coupon paymens from non-defauled asses whch have been reprced o reflec he ncrease n cred rsk and rsk-free neres raes. To esmae expeced ne profs we also need o forecas he fuure cash flows ha he bank needs o pay on s lables. As for CFA we have o make an assumpon on he re-nvesmen behavour, hs me wheher deposors are wllng o roll over her funds. In lne wh our prevous reasonng we assume ha deposors are wllng o roll over her deposs unless he bank defauls on s oblgaons. Gven we assume no sraegc defaul hs s only he case f eher he earnngs or he economc value condon s no me. Smlar o equaon (15), CFL evolves n lne wh A CFL = M j = 1 T b = C j, b L j, b b = 1 l = 1 I C l j, b l L j, b 1 (17) wh: I l =1 n perod l when lables n bucke b have been reprced he las me pror o I l = oherwse 11

12 As for asses, equaon (17) sums over all lably classes wh he frs par n brackes summng he coupon paymens of lably classes whch have no been reprced a me and he second par summng coupon paymens of lably classes whch have been reprced he las me n perod l pror o me. Takng equaons (14) o (17) allows us o forecas ne profs and hence he evoluon of shareholder funds. Rewrng Equaon (12) he change n shareholder funds s gven by: ΔSF = θ max ;( + mn ;( [ CFA CFL WR + OI Cos) ] [ CFA CFL WR + OI Cos) ] Whereas shareholder funds change n lne wh wre-offs and ncome, asses wll only vary n lne wh wre-offs (as shown n equaon (14). To balance he balance shee we assume ha he bank wll pay back deposs wh he free cash flows and n cases where shareholder funds decrease by more han wre-offs we assume ha he bank s able o arac new deposs. Therefore, (18) Δ FVL = ΔL = ΔA ΔSF = WR ΔSF (19) Our behavoural assumpons are o a ceran degree arbrary. Bu we resrc ourselves o specfc nvesmen rules raher han lookng a a bank whch re-opmses s porfolo n a mean-varance sense n each perod as hs would be beyond he scope of hs paper. 3 Sress esng cred and neres rae rsk for a sylsed bank The heorecal framework oulned above s flexble enough o accommodae sandard cred and neres rae rsk models as long as dfferen buldng blocks are muually conssen. I s essenal ha underlyng correlaons are capured - beween PDs of dfferen asse classes bu also beween PDs and he rsk-free yeld curve. A porfolo model based on Jarrow and Turnbull (2) would for example f hese requremens. In hs paper we use he sress esng model descrbed n Bunn e al (25) amended by he yeld curve model of Debold e al (26), esmaed on UK daa by Kubelec (26). Before urnng o he resuls hs secon descrbes he composon of he balance shee of he hypohecal bank and dscusses he sress esng and yeld curve model n more deal. 3.1 The hypohecal bank As an example for hs paper we consruc a hypohecal bank wh a hghly sylsed balance shee wh fve asse classes, hree lably classes, shareholder funds and neres rae swaps as off-balance shee ems (see Table A1 n he Appendx). We allocae asses, lables and off balance-shee ems no fve reprcng buckes and we refer o he reprcng msmach beween hem as neres rae sensvy gaps For off-balance shee ems we assume no counerpary rsk and herefore model hem as rsk-free nsrumens. 12

13 Alhough our balance shee s a hypohecal consruc we ensure ha he neres rae sensvy gap, shareholder funds, profably (n erms of reurn on equy and on asses), operang coss and he neres rae sensvy gap roughly maches a UK bank. As shown n Table A1 he reprcng buckes are no of equal sze wh respec o he lengh of me. We assume ha he frequency of me s quarerly and ha he exposure of he bank o an asse n a parcular reprcng bucke s equally spl beween he number of quarers whn he bucke. The upper lm of he las reprcng bucke s fve years and above. To enable us o allocae asses o quarerly buckes we assume ha he maxmum me-o-reprcng s en years and hus dvde he las me-bucke no 2 quarers beween he 5 h and 1 h year o reprcng. 3.2 The rsk-free erm srucure of neres raes We look a UK spo neres raes wh maures from 3 monhs o 1 years exraced from he Bank of England yeld curve daa se 15. The yeld curve daa are esmaed by fng a splne hrough general collaeral REPO raes and convenonal governmen bonds. We use he erm-srucure model by Debold e al (26) wh hree laen facors and hree observable macroeconomc varables. In vecor form, he sae-space sysem of he vecor of laen and observable varables, f, s gven by he vecor auoregresson of order 1: f μ = Φ( μ) + η (2) f The hree laen facors have he usual nerpreaon as he level, slope and curvaure of he yeld curve. The vecor of yelds, facors by: y, wh dfferen maures s relaed o he laen and observable macro y = Γ + ε, (21) f where Γ conans one free parameer and he yelds are assumed only o be affeced by he hree laen facors. Approprae zero resrcons are hus mposed on Γ. The ranson and measuremen dsurbances are assumed orhogonal o one anoher wh: η Δ ~ N, ε Π whereas Δ s no consraned, Π s dagonal and hence he nnovaons across yelds are assumed o be ndependen. The hree observable macroeconomc varables are he oupu-gap, nflaon and he Bank of England base rae 16. The model s esmaed on UK daa by Kubelec (26) usng monhly daa beween 1986 and 25. The esmaed erm-srucure model enables us o forecas he rsk-free yeld curves across maures up o en years condonal on a gven macro scenaro. LIBOR s hen forecased by assumng a consan spread over he rsk-free erm srucure of 3 bass pons. (22) 15 See Anderson and Sleah (1999). Daa are avalable from 13

14 3.3 Modellng PDs and LGDs for dfferen asse classes The prevous dscusson hghlghs ha macro facors are mporan drvers of he yeld curve. I has also long been undersood ha macroeconomc facors are mporan drvers of cred rsk (see Duffe and Sngleon, 23). In conras o mos cred rsk models our adoped approach has he benef ha explcly models he correlaon beween he sysemac rsk drvers of cred rsk and neres rae rsk as macroeconomc facors. Ths allows us o underake a scenaro analyss and smulae he economc value as well as profs for normal and hghly adverse economc condons. To capure he neracon beween macroeconomc shocks and cred rsk we buld on a sress esng model descrbed n Bunn e al (25). The models for corporae and household secor PDs were orgnally developed by Beno e al (21) bu exended work has been underaken by Whley and Wndram (23), Bunn and Young (24) and Whley e al (24). They use smple regresson echnques o lnk he probably of defaul o macro economc varables. Hence, for each of he dfferen asse class, he expeced probably of defaul s lnked o macroeconomc varables by: E ( PD 1, 1) = Ψ( X, ˆ) β (23) The funcon Ψ( ) ndcaes ha he expeced probably of defaul may be non-lnearly relaed o a vecor of explanaory varables, X, and a vecor of esmaed coeffcens, βˆ. The expeced corporae probably of defaul s modelled as a funcon of own lagged values, changes n he logarhm of GDP, corporae ncome gearng, he change n commercal propery capal values, frs dfference of he real neres rae and he rao of ne deb of PNFCs o nomnal GDP. Smlarly he expeced probably of defaul on morgage loans s modelled as a funcon of morgage ncome gearng, unemploymen, undrawn housng equy and LTV s he loan o value rao of frs me buyers. Fnally he expeced probably of defaul on cred card loans s modelled as a funcon of household ncome gearng and he number of acve cred balances. Seasonal dummes are also found sgnfcan n explanng he probably of defaul on cred card loans. For all ypes of household and corporae lendng, ncome gearng a measure of he ease wh whch households and frms can cover deb-servcng oblgaons s found o be an mporan drver of he probably of defaul. Income gearng n urn s hghly sensve o changes n neres raes. Ths mples ha he neres rae wll no only deermne he ne neres ncome bu s one of he key drvers of defaul rsk. GDP and unemploymen are addonal sgnfcan explanaory varables. The probably of defaul on corporae and morgage loans s also found o be affeced by he prces of commercal and resdenal propery respecvely. In our man smulaon we assume ha he LGD s fxed and no changng from he baselne o he sress scenaro. Bu we wll assess he mpac of changng LGDs n our sensvy analyss. Slghly worse han average ndusry numbers sugges, we assume ha he LGD on ner-bank loans s 4%, he LGD on morgage loans o be 3%, he LGD on cred cards o be 8% and he LGD on corporae loans o be 6%. 16 Ths ype of model does no mpose he no-arbrage condon across yelds wh dfferen maures (see, for example Ang e al, 26, or Lldhold e al, 26). Bu he model should sll be gvng a reasonably good forecas of he erm srucure based on a gven macro scenaro. 14

15 3.4 Modellng lables As dscussed n he framework secon s well known (Maes, 25) ha shorer-erm cusomer depos raes are generally below he rsk-free neres rae. Ths may be a resul of depos nsurance schemes, operaonal coss and barrers o enry lmng compeon. Whle an economc raonalsaon of negave spreads can be found for shor maures s no convncng for medum o long maures. We assume ha as he me-o-reprcng ncreases he neres pad by he bank on deposs gradually converges o he rsk-free neres rae. We model he depos rae on household deposs wh one quarer o reprcng o be 2% below he REPO rae and he corporae depos rae o be 1% below he LIBOR rae. The negave spreads are hen assumed o declne lnearly o be zero n he fourh quarer. 3.5 Forecasng sysemac rsk facors To be able o forecass PDs and yeld curves we need a model ha forecass and capures he correlaon of sysemac rsk facors beween each oher and across me. Raher han usng a smple macro VAR model whch would f hs requremen we use he Bank of England s macro model. Ths allows us o use he Bank of England Inflaon Repor forecass as baselne scenaro. As dscussed above s necessary o consder he sably of he bank n he shor and medum as well as he long erm. We choose he medum erm o be hree years. For a gven macro scenaro we forecas he dynamcs of he macro economy and map heses no PD forecass over he nex hree years usng he models dscussed n Secon Resuls In he hs secon we measure he mpac n he baselne and sress scenaro of cred rsk, neres rae rsk and her neracon on he economc value and he profably of our represenave bank over a hree year horzon. 4.1 The scenaros We follow Bunn e al (25) and look a he combnaon of hree shocks orgnally used for he IMF Fnancal Sably Assessmen Programme (FSAP) n 22: a 12% declne n UK resdenal and commercal propery prces, a 1.5% unancpaed ncrease n UK average earnngs growh and a 15% unancpaed deprecaon n he rade weghed serlng exchange rae. Indvdual scenaros are descrbed n Appendx A1. Orgnally, he magnudes of he ndvdual shocks have been calbraed o exreme evens relave o her hsorcal dsrbuon, and combnng hem begs he queson abou he lkelhood of such an even occurrng. One could use he hsorc covarance marx o deermne he probably of a combnaon of hese shocks happenng. Bu Bunn e al (25) do no 17 Afer he hrd year we assume ha he probably of defaul of each asse class revers back o s long run level over he followng en years. The quarerly probably of defaul on corporae loans hus revers o.35%, on morgage loans o.7% and on cred cards o.61%. These assumpons are no gong o be srongly decsve for he resuls presened n he nex secon. Resuls of hs sensvy es can be provded by he auhors on reques. 15

16 aemp hs and approach as a purely mechancal exercse. Unsurprsngly, he combnaon of shocks has a greaer mpac han each of he ndvdual shocks alone. All our scenaros are run from 25 Q1 and forecased over a hree year horzon. As base case scenaro we use he Bank of England February 25 Inflaon Repor s projecons where neres raes are assumed o follow marke expecaons. When runnng he combnaon of shocks hrough he macro model, we do no apply any judgemens and we smply apply he shocks mechancally. As wll become apparen, and a he hear of hs paper, he key macroeconomc varable s he neres rae. Hence, modellng he moneary polcy reacon o he nal shock s crucal. In lne wh general macro sress esng pracces we assume a mechancal Taylor rule Rsk-free and cred spread yeld curves In Fgure A1 n he Appendx we compare he evoluon of he rsk-free yeld curves over he nex hree years n he baselne and sress scenaro. Whereas n boh cases he rsk-free yeld curve s downward slopng, he ncrease n he level followng he sress s evden across all maures. Furhermore, he yeld curve flaens n he sress scenaro wh he shor end of he curve around 5.5% n he frs quarer ncreasng seadly over he hree years reachng almos 1% hree years afer he shock. In Fgure 1 we show he cred spread curves for morgages, corporae and cred cards. The sold lnes represen he spreads afer one quarer n he base case and he dashed lnes he spreads one quarer afer he shock (ndcaed by 1 n Fgure A1). As defaul raes and LGDs on cred cards are hghes, spreads on cred card lendng are much hgher han for lendng o (secured) households or corporaes. In he base case spreads on morgages are n lne wh average morgage raes currenly observed n he marke place. Spreads on corporaes compare o a BBB spread whch s slghly above he average qualy (BB) of he corporae porfolo of a ypcal G1 bank (see Caarneu- Rabell, e al, 23). 18 Under a Taylor rule, neres raes are modelled as a lnear combnaon of devaons of nflaon from a arge rae and oupu from poenal oupu. Ths reamen s, of course, no represenave of he way n whch he Moneary Polcy Commee ses neres raes. As has been descrbed by he Bank of England elsewhere, Commee members use a range of models and judgemens n formng her assessmens. 16

17 Fgure 1: Annualsed cred spread curves before end afer he sress 4.5 Per cen 5 Morgage Sress Cred Cards Sress Corporae Sress Morgage Base Cred Card Base Corporae base Tme-o-maury The larges ncrease n spreads n he sress scenaro occurs for morgages. Alhough he spread on cred cards does no rse by as much, remans hgher han ha for morgages. The corporae spread s leas affeced by he macroeconomc shock. The man reason for he subdued rse n he corporae spread s conssen wh he relavely hgh cred qualy of he banks corporae lendng book. 4.3 Condon 1: he economc value perspecve As posulaed n he framework secon we adop an economc value perspecve o measure he poenal long-erm mpac of he shock on he bank. The economc value of our hypohecal bank n he baselne scenaro s calbraed o 7.3% of he face value of asses. Ths equals he book value of asses ne of lables and ne off-balance shee ems. Immedaely afer he shock crysallses he economc value falls o 5.7% of he face value of asses. Even hough hs represens a 21% fall n economc value, he long-erm combned mpac of cred and neres-rae rsk s no large enough o hreaen he sably of he hypohecal bank. 4.4 Condon 2: he earnngs perspecve Gven he severe naure of he shocks may sll be he case ha n he shor or medum erm he bank makes losses whch could hreaen s capal. For hs reasons s mporan o nvesgae wheher Condon 2 s sasfed, ha s wheher he bank s expeced capal adequacy remans above he regulaory mnmum n all perods n he medum erm,.e. he nex hree years. As descrbed n he framework secon Condon 2 depends, ner ala, on he evoluon of ne profs, shareholder funds and rsk weghed asses. In urn he key wo deermnans of ne profs are ne neres ncome and wre-offs. In lne wh Bunn e al (25) wre-offs are sgnfcanly hgher n he sress scenaro and peak afer around 2 ½ years (doed lnes n Fgure 2). Ths ncrease n cred rsk s also refleced n he ncreasng cred spreads n Fgure 1. 17

18 Inally, ne neres ncome falls slghly due o a rse n borrowers defaulng as well as o he margn compresson beween shor erm borrowng and long erm lendng raes (sarred lnes n Fgure 2). However, afer 1 ½ years, ne neres ncome sars o ncrease up o he 12h quarer when fully offses he hgher wre-offs and neres raes. The ncrease n ne neres ncome follows he gradual reprcng of asses reflecng he hgher cred rsk n he sress scenaro 19. Fgure 2: Evoluon of quarerly ne profs, ne neres ncome and wre-offs Fgure 3: Evoluon of annualsed reurn on equy per quarer (RoE) Wre-offs - base scenaro Ne neres ncome - base scenaro Ne prof - base scenaro Wre-offs - sressed scenaro Ne neres ncome - sressed scenaro Ne prof - sressed scenaro Per cen Quarers ahead 5 Base scenaro Sress scenaro Quarers ahead The combned mpac of wre-offs and ne neres ncome mply ha ne profs (sold lne n Fgure 2) fall by abou 5% n he sxh quarer bu recover o he base lne afer 3 years. As we wll dscuss n more deal n he nex secon Fgure 2 already ndcaes ha neres rae and cred rsk have o be assessed jonly. For example, focusng on pure defaul rsk by only lookng a wre-offs leads o an underesmaon of rsk n he shor erm and an overesmaon of rsk n he long run. To capure rsks fully, he nal margn compresson and he subsequen reprcng has o be aken no accoun. The mpac of he shock can also be summarzed n erms of reurn on equy (RoE) as llusraed n Fgure 3. Compared o a roughly consan RoE of 2% n he base lne scenaro, he shock halves he bank s RoE n he wors quarer. Bu s also evden how he bank remans profable n every quarer over he hree-year horzon. As profs afer ax and dvdends are reaned as capal, shareholder funds ncrease n each quarer. And gven ha under he sandardsed approach rsk weghs do no adjus o he decrease n cred qualy, Condon 2a mproves n boh scenaros as shown n Fgure 4, Panel A. Conversely, under he nernal approach he ncrease n shareholder funds s more han offse by he ncrease n rsk weghs reflecng he rse n cred rsk (Fgure 4, Panel B). However, he overall fall does no hreaen he sably of he bank as he capal rao always remans well above he regulaory mnmum. As well as Condon 2a, Condon 2b s herefore sasfed n all perods. 19 Noe ha we are assumng ha he bank can fully ranslae he ncrease n PDs no he prema charges on borrowers, and ha such a rse n prema does no affec wre-offs and arrears. 18

19 Overall, we can conclude ha ndependenly of wheher we look a he shor or long run ndcaors developed n hs paper, he shock would weaken our hypohecal bank bu would no hreaen s sably. Fgure 4: Shareholder funds as a proporon of rsk-weghed asses Condon 2 Panel A: Panel B: Condon 2a: Consan-rsk-wegh approach Condon 2b: Inernal approach Per cen Regulaory mnmum Quarers ahead Base scenaro Sressed scenaro Per cen Regulaory mnmum Base scenaro Sressed scenaro Quarers ahead 5 Inegraon of neres and cred rsk Gven neres rae and cred rsk are nrnscally relaed, hs secon nvesgaes whch rsk s he man drver of he fall n profs n he sress scenaro. For hs analyss we break down he mpac no hree componens: A. The mpac of cred rsk from non-neres rae facors. B. The mpac of neres rae rsk bu excludng he effec of changes n neres raes on cred rsk. C. The mpac of he neracon of cred rsk and neres rae rsk. To assess (A) we calculae PDs condonal on all sysemac rsk facors changng o her sressed levels bu neres raes remanng as n he base case scenaro. Hence, (A) hghlghs he mporance of all non-drec neres rae facors. (B) s smlar o neres sensvy analyss run by banks on he whole porfolo. As dscussed prevously, hese ess look a shfs (ofen only parallel ones) n he yeld curve bu gnore any mplcaons hs may have on cred rsk. (C) s calculaed as he dfference beween he mpac of he overall shock, as descrbed n he prevous secon, and he combned mpac of (A) and (B). Fgure 5 shows ha n comparson o oher macroeconomc facors neres raes are he key drver of he rse n cred rsk n our scenaro. Fgure 6 dsenangles he complex effecs of neres rae and cred rsk on ne neres ncome. As gap-analyss suggess pure neres rae rsk decreases ne 19

20 neres ncome as margns are compressed. However, pure neres rae rsk does no ake accoun of he mpac of neres raes on cred qualy nor he correlaon of neres raes and oher cred rsk drvers n a sressed scenaro. The ncrease n cred rsk has wo effecs on ne neres ncome. Frs, hgher wre-offs decrease ne neres ncome as he bank s exposures declne over me. Bu second, hs effec s ouweghed by he posve mpac of cred rsk on ne neres ncome because, over me, banks adjus he cred spread on loans ha are reprced. 2 Lookng a he overall mpac on profs (Fgure 7) s evden ha he rse n neres raes s he man drver of he fall n ne profs reflecng he combned effec of he squeeze n ne margns and he rse n wre-offs caused by he change n neres raes. Hence, he combned mpac of correlaed cred and neres-rae rsk s he key deermnan of he banks rsk profle. Ths dscusson hghlghs why rsks have o be assessed jonly. For example, a smple gap analyss s no suffcen for rsk assessmen as hs only looks a he srped area n Fgure 6 gnorng all oher effecs on ne profs. Smlarly, focusng on cred qualy only, for example by projecng expeced wre-offs, s also msleadng. Such an analyss does no accoun for he nal fall and subsequen ncrease n ne neres ncome as shown n Fgure 6. 2 Even hough ne neres ncome falls n he frs quarer due o some loans defaulng hs effec s neglgble. Bu he small mpac on ne neres ncome n hs quarer s drven by our assumpon ha he shores reprcng maury s 3 monhs across all asse and lably classes. Shorer maures such as overngh bank deposs would only lead o a bgger decrease n ne-neres ncome n he frs quarer bu would no change he remander of he analyss. 2

21 Fgure 5: Impac on wre offs (a) Quarers ahead Ineracon of cred and neres rae rsk Cred rsk from nonneres rae facors (a) The scale s nvered o vsually enable he addng of wre-offs and ne neres ncome Fgure 6: Impac on ne neres ncome Quarers ahead Ineracon of cred and neres rae rsk Ineres rae rsk excludng mpac on cred rsk Cred rsk from non neres rae facors Ne mpac Fgure 7: Impac on profs Quarers ahead Cred rsk from nonneres rae facors Ineracon of cred and neres rae rsk Ineres rae rsk excludng mpac on cred rsk 21