The Sensitivity of Bank Net Interest Margins and Profitability to Credit, Interest-Rate, and Term-Structure Shocks Across Bank Product Specializations

Transcription

1 The Sensiiviy of Ban Ne Ineres Margins and Profiabiliy o Credi, Ineres-Rae, and Term-Srucure Shocs Across Ban Produc Specializaions Gerald Hanwec Professor of Finance School of Managemen George Mason Universiy Fairfax, VA ghanwec@gmu.edu and Visiing Scholar Division of Insurance and Research FDIC Lisa Ryu Senior Financial Economis Division of Insurance and Research FDIC lryu@fdic.gov January 2005 Woring Paper The auhors wish o han paricipans a he FDIC s Analys/Economiss Conference, Ocober 7 9, 2003, and a he Research Seminar a he School of Managemen, George Mason Universiy, for helpful commens and suggesions. The auhors would also lie o han Richard Ausin, Mar Flannery, and FDIC Woring Paper Series reviewers for heir commens and suggesions. All errors and omissions remain he responsibiliy of he auhors. The opinions expressed in his paper are hose of he auhors and do no necessarily reflec hose of he FDIC or is saff.

2 The Sensiiviy of Ban Ne Ineres Margins and Profiabiliy o Credi, Ineres-Rae, and Term-Srucure Shocs Across Ban Produc Specializaions Absrac This paper presens a dynamic model of ban behavior ha explains ne ineres margin changes for differen groups of bans in response o credi, ineres-rae, and erm-srucure shocs. Using quarerly daa from 1986 o 2003, we find ha bans wih differen produc-line specializaions and asse sizes respond in predicable ye fundamenally dissimilar ways o hese shocs. Bans in mos ban groups are sensiive in varying degrees o credi, ineres-rae, and erm-srucure shocs. Large and more diversified bans seem o be less sensiive o ineres-rae and erm-srucure shocs, bu more sensiive o credi shocs. We also find ha he composiion of asses and liabiliies, in erms of heir repricing frequencies, helps amplify or moderae he effecs of changes and volailiy in shor-erm ineres raes on ban ne ineres margins, depending on he direcion of he repricing mismach. We also analyze subsample periods ha represen differen legislaive, regulaory, and economic environmens and find ha mos bans coninue o be sensiive o credi, ineres-rae, and erm-srucure shocs. However, he sensiiviy o erm-srucure shocs seems o have lessened over ime for cerain groups of bans, alhough he resuls are no universal. In addiion, our resuls show ha bans in general are no able o hedge fully agains ineres-rae volailiy. The sensiiviy of ne ineres margins o ineres-rae volailiy for differen groups of bans varies across subsample periods; his varying sensiiviy could reflec ineres-rae regime shifs as well as he degree of hedging aciviies and mare compeiion. Finally, by invesigaing he sensiiviy of ROA o ineres-rae and credi shocs, we have some evidence ha bans of differen specializaions were able o price acual 1

3 and expeced changes in credi ris more efficienly in he recen period han in previous periods. These resuls also demonsrae ha bans of all specializaions ry o offse adverse changes in ne ineres margins so as o mue heir effec on repored afer-ax earnings. 2

4 1. Inroducion The baning indusry has undergone considerable srucural change since he early 1980s as he legislaive and regulaory landscape governing he indusry has evolved. The srucural changes, in urn, have had significan effecs on he degree of mare compeiion and he scope of producs and services provided by bans as well as significan effecs on he sources of ban earnings. Despie hese developmens, credi and ineres-rae riss sill largely accoun for he fundamenal riss o ban earnings and equiy valuaion as well as o he coningen liabiliy borne by he FDIC insurance funds. The relaive imporance of credi and ineres-rae riss for ban earnings and he FDIC s coningen liabiliy has varied over ime in response o changes in he macroeconomic, regulaory, and compeiive environmens. 1 Despie he rising imporance of fee-based income as a proporion of oal income for many bans, ne ineres margins (NIM) remain one of he principal elemens of ban ne cash flows and afer-ax earnings. 2 As shown in figure 1, excep for very large insiuions and credi card specialiss, nonineres income sill remains a relaively small and usually more sable componen of ban earnings. As a resul, despie earnings diversificaion, variaions in ne ineres income remain a ey deerminan of changes in profiabiliy for a majoriy of bans. However, research in he area of ban ineres-rae ris and he behavior of NIM has been largely limied since he lae 1980s, when he savings and loan crisis brough he issue of ineres-rae ris o he fore. Undersanding he sysemaic effecs of changes in ineres-rae and credi riss on ban NIM will liely help he FDIC beer prepare for variaions in is coningen liabiliy associaed wih adverse developmens in he macroeconomic and financial mare environmen. 1 For example, Duan e al. (1995) posi ha ineres-rae ris dominaed he volailiy of he FDIC s coningen liabiliies in he early 1980s he ime of high ineres-rae volailiy whereas credi ris became he leading facor in he lae 1980s and early 1990s, as ineres-rae volailiy subsided. 2 Throughou his paper, ne ineres margins are defined as annualized quarerly ne ineres income (ineres income less ineres expense) as a raio of average earning asses. 3

5 The objecive of his paper is wofold. Firs, his paper develops a new dynamic model of ban NIM ha reflecs he managerial decision process in response o credi, ineres, and ermsrucure shocs. We focus our analysis primarily on variaions in ne ineres margins, alhough ban managers adjus heir porfolios in order o manage repored afer-ax profi raher han ne ineres margins. However, given ha he variaion in ne ineres income is he ey deerminan of earnings volailiy for many bans, undersanding he degree o which hese shocs affec he ban s ne ineres income would help us idenify he channels hrough which hey could affec overall ban profiabiliy and he responses baners mae o manage repored profiabiliy. The degree o which he ban can change he porfolio mix and/or hedge in he shor erm would deermine he magniude of he effec of ineres-rae changes and oher shocs on ban profiabiliy. Our second objecive is o use a large se of daa, consising of quarerly ban and financial mare daa from firs quarer 1986 o second quarer 2003, o evaluae he model. In addiion, we invesigae wheher he sensiiviy o shocs varies across diverse ban groups on he basis of heir produc-line specializaions as well as differen regulaory regimes. We focus on he effecs of hree ey legislaive changes on ban NIM during he sample period: he Deposiory Insiuions Deregulaion and Moneary Conrol Ac (DIDMCA) of 1980, which se in moion he phasing ou of he Regulaion Q ceilings on deposis; he Federal Deposi Insurance Corporaion Improvemen Ac (FDICIA) of 1991; and he Riegle-Neal Inersae Baning and Branching Efficiency Ac (Riegle-Neal) of 1994, which became effecive in July These pieces of legislaion have liely changed he sensiiviy of ban NIM o credi, ineres-rae, and erm-srucure shocs, for hey spurred price compeiion for deposis ha 3 See FDIC (1997) for a deailed discussion of he legislaive and regulaory hisory of he baning crisis of he 1980s and early 1990s. 4

6 reduced volailiy in ban lending, improved he capial posiions of bans, allowed geographic and earnings diversificaion, and changed he general compeiive landscape. No empirical sudy o dae has invesigaed he effecs of hese legislaive changes on he behavior of ban NIM. Empirical evidence and casual observaion reinforce he view ha bans wih differen produc-line specializaions end o have disincive business models and corresponding rismanagemen pracices and characerisics. In addiion, bans wih differen produc-line specializaions also face differen compeiive landscapes, wih some ban groups experiencing progressively more inense compeiion han ohers. To maximize profiabiliy and enhance ban value, baners aemp o choose a produc mix ha bes fis heir perceived mares and managerial experise, hus gaining a compeiive advanage for lending, invesing, and raising funds hrough deposis. For mos bans, he choice of mare means some degree of specializaion in paricular produc lines and geographic locaions. The ban porfolios associaed wih hese various produc lines are liely o exhibi differen degrees of sensiiviy o ineres-rae and credi-ris changes. The exen o which baners can offse adverse ineres-rae changes and hedge adverse credi-ris changes will depend on he principal produc line of he ban, he flexibiliy of he porfolio in responding o change, and he cos and availabiliy of hedges for a paricular porfolio. Our empirical resuls show ha ne ineres margins associaed wih some ban porfolios derived from specializing in cerain produc lines are considerably more sensiive o ineres-rae changes han ohers. The magniude of hese effecs depends on he repricing composiion of exising asses and liabiliies: bans ha have a higher proporion of ne shor-erm asses in heir porfolio experience a greaer boos in heir NIM as ineres raes rise. We find ha changes in ban ne ineres margins are ypically negaively relaed o ineres-rae volailiy bu posiively 5

7 relaed o increases in he slope of he yield curve. Changes in he yield spread have significan and lingering effecs on NIM for many ban groups, bu he effecs are paricularly noable for morgage specialiss and small communiy bans. We find ha, for mos ban groups, afer-ax earnings are less sensiive o ineres-rae changes han NIM are, bu he degree of sensiiviy differs among bans wih differen produc-line specialies. We find ha ban NIM are negaively relaed o an increase in realized and expeced credi losses, paricularly among bans specializing in commercial-ype loans (i.e., commercial and indusrial loans and commercial real esae loans). We posi ha his inverse relaionship beween realized credi ris, as indicaed by an increase in nonperforming loans, and ne ineres margins exiss because, in he shor run, ris-averse ban managers reallocae heir funds o less defaul-risy, lower-yielding asses in response o an increase in he credi ris of heir porfolios. This response is reinforced by ban examiners, who encourage bans o reduce heir exposure o risy credis when loan qualiy is observed o be deerioraing. Bans ne ineres margins are posiively relaed o a size-preserving increase in high-yielding, and presumably higher-ris, loans. We generally find ha he esimaed parameers of he models differ by subperiod for bans wih differen produc-line specialies in ways ha are saisically and economically meaningful. This paper exends he exising lieraure on NIM in hree imporan respecs. Firs, we develop a dynamic behavioral model of variaions in NIM in response o mare shocs ha more closely resembles he acual decision-maing process of ban managers han exising models. Second, by reaing he baning indusry as inherenly heerogeneous (which we do by dividing bans ino groups based on heir produc-line specializaions), we are able o proxy broad differences in business models and managerial pracices wihin he baning indusry, and 6

8 idenify groups of bans ha are mos sensiive o credi, ineres-rae, and/or erm-srucure shocs. Finally, we are able o es he imporance of shifs in regulaory regime in behavioral differences across subperiods for he same group of bans. The res of he paper is organized as follows: secion 2 reviews he lieraure relaing o ineres effecs on ban ne ineres margins; secion 3 presens a heoreical model of ban behavior in response o ineres-rae shocs; secion 4 discusses he daa, he empirical variables, and he empirical specificaions for he model; secion 5 presens he resuls of boh he full sample period and he subsample periods; and secion 6 concludes he paper. 2. Lieraure Review Despie significan regulaory concern paid o he ineres-rae ris ha bans face (OCC [2004]; Basel Commiee on Baning Supervision [2004]), research on a ey componen of earnings ha may be mos sensiive o ineres shocs namely, ban ne ineres margins has been limied hus far, paricularly for U.S. bans. Wih a few excepions discussed in his secion, here has been lile published research on he effecs of ineres-rae ris on ban performance since he lae 1980s. Theoreical models of ne ineres margins have ypically derived an opimal margin for a ban, given he uncerainy, he compeiive srucure of he mare in which i operaes, and he degree of is managemen s ris aversion. The fundamenal assumpion of ban behavior in hese models is ha he ne ineres margin is an objecive o be maximized. In he dealer model developed by Ho and Saunders (1981), ban uncerainy resuls from an asynchronous and random arrival of loans and deposis. A baning firm ha maximizes he uiliy of shareholder wealh selecs an opimal marup (mardown) for loans (deposis) ha minimizes he riss of surplus in he demand for deposis or in he supply of loans. Ho and 7

9 Saunders conrol for idiosyncraic facors ha influence he ne ineres margins of an individual ban, and derive a pure ineres margin, which is assumed o be universal across bans. They find ha his pure ineres margin depends on he degree of managemen ris aversion, he size of ban ransacions, he baning mare srucure, and ineres-rae volailiy, wih he rae volailiy dominaing he change in he pure ineres margin over ime. Allen (1988) exends he single-produc model of Ho and Saunders o include heerogeneous loans and deposis, and posis ha pure ineres spreads may be reduced as a resul of produc diversificaion. Saunders and Schumacher (2000) apply he dealer model o six European counries and he Unied Saes, using daa for 614 bans for he period from 1988 o 1995, and find ha regulaory requiremens and ineres-rae volailiy have significan effecs on ban ineres-rae margins across hese counries. Angbazo (1997) develops an empirical model, using Call Repor daa for differen size classes of bans for he period beween 1989 and 1993, incorporaing credi ris ino he basic NIM model, and finds ha he ne ineres margins of commercial bans reflec boh defaul and ineres-rae ris premia and ha bans of differen sizes are sensiive o differen ypes of ris. Angbazo finds ha among commercial bans wih asses greaer han $1 billion, ne ineres margins of money-cener bans are sensiive o credi ris bu no o ineres-rae ris, whereas he NIM of regional bans are sensiive o ineres-rae ris bu no o credi ris. In addiion, Angbazo finds ha off-balance-shee iems do affec ne ineres margins for all ban ypes excep regional bans. Individual off-balance-shee iems such as loan commimens, leers of credi, ne securiies len, ne accepances acquired, swaps, and opions have varying degrees of saisical significance across ban ypes. 8

10 Zarru (1989) presens an alernaive heoreical model of ne ineres margins for a baning firm ha maximizes an expeced uiliy of profis ha relies on he cos of goods sold approach. Uncerainy is inroduced o he model hrough he deposi supply funcion ha conains a random elemen. 4 Zarru posis ha under a reasonable assumpion of decreasing absolue ris aversion, he ban s spread increases wih he amoun of equiy capial and decreases wih deposi variabiliy. Ris-averse firms lower he ris of profi variabiliy by increasing he deposi rae. Zarru and Madura (1992) show ha when uncerainy arises from loan losses, deposi insurance, and capial regulaions, a higher uncerainy of loan losses will have a negaive effec on ne ineres margins. Madura and Zarru (1995) find ha ban ineresrae ris varies among counries, a finding ha suppors he need o capure ineres-rae ris differenials in he ris-based capial requiremens. However, Wong (1997) inroduces muliple sources of uncerainy o he model and finds ha size-preserving increases in he ban s mare power, an increase in he marginal adminisraive cos of loans, and mean-preserving increases in credi ris and ineres-rae ris have posiive effecs on he ban spread. Boh he dealer and cos-of-goods models of ne ineres margins have wo imporan limiaions. Firs, hese models are single-horizon, saic models in which homogenous asses and liabiliies are priced a prevailing loan and deposi raes on he basis of he same reference rae. In realiy, ban porfolios are characerized by heerogeneous asses and liabiliies ha have differen securiy, mauriy, and repricing srucures ha ofen exend far beyond a single horizon. As a resul, assuming ha baners do no have perfec foresigh, decisions regarding loans and deposis made in one period affec ne ineres margins in subsequen periods as bans face changes in ineres-rae volailiy, he yield curve, and credi ris. Bans abiliy o respond 4 Uncerainy in he ban s deposi supply funcion is modeled as D * = D( RD ) + µ where R D is he ineres rae on deposis and µ is a random erm wih a nown probabiliy densiy funcion. 9

11 o hese shocs in he period is consrained by he ex ane composiion of heir asses and liabiliies and heir capaciy o price changes in riss effecively. In addiion, he credi cycle and he srengh of new loan demand deermine he magniude of he effec of ineres-rae shocs on bans earnings. In his regard, Hasan and Sarar (2002) show ha bans wih a larger lending slac, or a greaer amoun of loans-in-process, are less vulnerable o ineres-rae ris han bans wih a smaller amoun of loans in process. Empirical evidence, using aggregae ban loan and ime deposi (CD) daa from 1985 o 1996, indicaes ha low-slac bans indeed have significanly more ineres-rae ris han high-slac bans. The model also maes predicions regarding he effec of deposi and lending rae parameers on ban credi availabiliy ha were no empirically esed wih aggregae daa. The second imporan limiaion of boh he dealer and cos-of-goods models of ne ineres margins is ha hey rea he baning indusry eiher as being homogenous or as having limied heerogeneous rais based only on heir asse size. However, bans wih disinc producion-line specializaions usually differ in erms of heir business models, pricing power, and funding srucure, all of which liely affec ne ineres margin sensiiviy o ineres-rae and oher shocs. For insance, in he 1980s and early 1990s, credi card ineres raes were ypically viewed as sicy or insensiive o mare raes, a view suggesing imperfec mare compeiion (Ausubel [1991]; Calem and Meser [1995]). This view would imply ha ne ineres margins of credi card bans, as a group, would be significanly less sensiive o ineresrae shocs han oher bans. Furlei (2003) documens noable changes in credi card pricing due o inense compeiion over he pas decade; however, i is no clear how hese changes have affeced credi card specialiss sensiiviy o ineres-rae and oher shocs. In comparison, morgage lenders, as a group, have a balance shee wih a significan mismach in he mauriy of 10

12 heir asses and liabiliies, and hey are herefore more liely o be sensiive o changes in he yield curve. 3. A Model of Ban Behavior Discussed in his secion is a model of he effecs of ineres-rae and credi ris changes using he mismaching of asse and liabiliy repricing frequencies. The model is a sandard approach o evaluaing changes in NIM due o changes in ineres raes and credi qualiy as loans ha are passed-due or charged off are essenially repriced in he curren period. 3.1 Ineres-Rae Changes The model of ban behavior relaing o ne ineres margins used in his paper assumes ha a each period a ban can significanly bu no compleely choose he amoun of is invesmen in asses and liabiliies of differen repricing frequencies, given pas choices ha are immuable. Admiedly, his is a fuzzy saemen as o he choices available o a ban, bu bans have a moderae degree of conrol over heir asse mix in he shor run (from quarer o quarer) by purchasing or selling asses of differen repricing frequencies. As suggesed above, bans choices of principal produc-line specializaions will deermine he mare condiions hey face ha may limi heir abiliy o mae rapid asse porfolio adjusmens. The same is rue for ban liabiliies. Baners can pay hem early, deposis can be received and wihdrawn a random, and some of hem, lie federal funds and repurchase agreemens, are under he conrol of he ban and can be changed overnigh. In conras o bans abiliy o mae porfolio adjusmens, bans have lile conrol over mare ineres-rae changes and ineres-rae volailiy. When conracs on asses or liabiliies 11

13 are negoiaed, bans may, hrough mare power, be able o se levels or marups (mardowns) over index raes such as LIBOR, bu are unable o conrol index rae changes. In addiion, we assume ha marups are conracually fixed in he shor run. Furhermore, bans are unable o change heir chosen produc-line specializaions in he shor run, so such changes are sraegic opions only. In our modeling of ban responses o credi and ineres-rae riss, we assume ha bans are mos ineresed in achieving he bes afer-ax profi performance hey can in order o provide shareholders wih maximum value. Maximizing shareholder value in a dynamic conex, however, is a dauning problem and requires considerable judgmen. No only do ban managers have o choose he opimal financial service produc mix (produc-line specializaion, in his sudy) and geographic diversificaion, bu hey also need o se he lending rae and fees, hedge credi qualiy and volailiy changes, manage heir liabiliy srucure, and gauge he moods of he equiy and deb mares o favorable or unfavorable news so as o increase or proec shareholder value. Given hese underlying condiions regarding bans moivaions and heir abiliy o change heir porfolios and heir posiions as ineres-rae aers, we assume ha bans operae such ha hey will change heir porfolio mix only o increase profis and maximize shareholder value over a 12-monh horizon. As discussed above, he ne ineres margin is he major source of ne income for mos bans, and herefore a sraegy of maximizing is value in he shor run may be a reasonable proximae goal for achieving maximum ban profis in he shor run. If ris-neural pricing were prevalen in financial mares, bans would all price loans in a similar way, and shor-run maximizaion of he expeced value of ne ineres margins would be a proper ban objecive. 5 However, bans can do beer. They can mae decisions as o he iming of 5 As poined ou in he inroducion, bans in general have been increasing fee income as a way o achieve greaer long-run profiabiliy. Fee income is difficul o adjus in he shor run in response o ineres-rae changes because 12

14 credi charge-offs, changing porfolios for credi ris purposes, and changing asse srucure by buying or selling liquid asses (U.S. governmen and agency deb). To bes consider he ineres-rae sensiiviy of ne ineres margin, we consider he ne ineres margin as a funcion of ineres raes on asses and liabiliies and he shares of each as a raio o earning asses a each repricing frequency. Throughou he developmen of he model, we are assuming ha he ban has chosen is produc-line specializaion and ha he asses and liabiliies reflec his choice for each ban. This relaionship can be formally saed as NIM p NII = p EA p m yea rl p =1 = (1) EA p where p refers o produc line p, NIM p is ne ineres margin in, NII is ne ineres income (ineres income less ineres expense) in, EA p is he amoun of ineres-earning asses in he porfolio in, y is he ineres rae on asses of repricing frequency, EA is he amoun of earning asses in repricing frequency, r is he ineres rae on liabiliies for repricing frequency, and L is he amoun of liabiliies for repricing frequency. Operaionally, he firs repricing frequency, for example, would be overnigh. Since NIM will be subjec o changes in ineres raes on earning asses and ineresbearing liabiliies, changes in individual invesmens in earning asses, funding from ineresbearing liabiliies and changes in he overall invesmen in earning asses, he coninuous change in NIM, dnim, is a funcion of hese ban managemen porfolio decisions and of ime. In general, his can be expressed more formally, assuming coninuous ime and using (1) for any produc line, as follows: of is longer-erm conracual basis. One excepion is for credi card bans, where fees can be modified a he will of he lender, as can ineres raes on ousanding balances of accumulaed ineres and original principal. 13

15 NIM NIM dnii NII dnim 2 = dnii + dea = dea (2) NII EA EA EA where he changes in NII and EA, dnii and dea, are he resul of changes in he ineres raes, dy and dr and ban managemen decisions on invesmens in EA. The produc-line index is dropped o simplify he noaion. Noing ha he oal derivaive of NII can be expanded in erms of ineres-rae, earning asse, and liabiliy changes: dnii NII NII = EA dy m m dy dr = = 1 y r = 1 + y dea L dr r dl (3) In his formulaion, we assume ha ineres-rae changes are independen of each oher, which is no usually he case. We can change his assumpion by subsiuing a erm-srucure and crediris spread facor model for each ineres-rae change. For he NIM modeling, we will use a more simplified approach ha can accommodae he erm-srucure and credi-ris spread effecs on NIM. Expressing he ineres change effecs on NIM, we subsiue (3) ino (2) for dnii resuling in dnim = m =1 EA dy + y dea EA L dr r dl NIM dea EA (4) Noe ha he final erm in (4) is he proporional change in EA over he preceding period imes he curren period NIM. This erm is negaively relaed o he change in NIM, implying ha if all oher facors are held consan, increases in earning asses will end o decrease he ne ineres margin. Wih respec o he firs erm in (4), consan ineres raes mean ha all dy and dr are zero such ha he proporion of each asse and liabiliy componen relaive o EA would have no effec on he change in NIM. Under hese ceeris paribus condiions, his erm is he raio of he 14

16 change in NII resuling from a change in each asse and liabiliy componen, wih each componen s proporion o EA held consan. If dea is posiive and each dea and dl grows a he same posiive rae as earning asses, he effec would be o increase NII such ha dnii was posiive as long as NIM was posiive. The ne effec on NIM under hese condiions is zero. The implicaion of his resul is imporan for inerpreing he effec of he growh in earning asses on bans' ne ineres margins. Wihou advanageous changes in ineres raes or changes in he composiion of asses and liabiliies relaive o earning asses, a growh in earning asses will have lile effec on NIM. Bans should experience an increase in NII by pracically he same proporion as EA. Therefore, managemen canno rely solely on growh o increase NIM or profiabiliy bu mus manage he composiion of asses and liabiliies o achieve greaer NIM and ROA, given managemen s expecaion of changes in ineres raes and erm srucure. To complee he model for esimaion, changes in ineres raes are assumed o be ouside he conrol of managemen and each is subjec o a coninuous ime, sochasic diffusion process as follows: dy = f ( y, ) d + σ dz (5) y where σ y is he sandard deviaion of changes in y, f(y,) is a drif erm or mean for dy, and dz is a Weiner process of ineres-rae changes wih repricing frequency. We assume, for simpliciy, ha each y and r follows he same sochasic processes so ha dz depends only on he repricing frequency,. Furhermore, he drif erm requires a hypohesis for is value. If i is hypohesized ha here is a endency of regression oward a mean (e.g., Vasice and Heah- Jarrow-Moron models), he sign of he erm will depend on wheher ineres raes are above or below he mean. Anoher hypohesis is ha he drif erm is zero because ineres raes follow a 15

17 random wal once regime shifs are complee (see Ingersoll [1987], 403). 6 Since we do no wish o impose an ineres-rae adjusmen hypohesis or a erm-srucure hypohesis on baners adjusmen o ineres-rae changes, we will allow he daa o provide esimaes of he effec of ineres-rae and erm-srucure changes. 7 These ineres-rae diffusion processes can be subsiued ino (4) for he final model: dnim = m = 1 EA f ( y, ) + EA σ dz + y dea L f ( r, ) y EA L σ dz r r dl NIM dea EA (6) The drif erms, f(y,) and f(r,), pose an ineresing way of viewing he sign of any esimaion of he coefficien on EA or L. If hese erms are zero and E(dz ) is zero, he effec of changes in earning asses is sricly condiioned by ineres rae changes. If ineres raes increase for asses and liabiliies wih repricing frequencies of less han one year, he change in NIM, all oher facors held consan, depends on he relaive shares of earning asses and liabiliies repricing wihin one year. If shor-erm liabiliies have a greaer proporion of EA han asses, dnim will be negaive and NIM will fall in he nex period. Noe also ha he effec of ineres-rae volailiy on NIM, σ y and σ r, will be in he same direcion as respecive ineres-rae changes, meaning ha higher ineres volailiy has he same relaionship as an increase in ineres raes depending on he sign of he repricing gap, he difference beween asses and liabiliies in he same repricing frequency, or cumulaive repricing frequencies. 6 The hypohesis of a random wal is perhaps mos appropriae for he period under analysis. From 1984 o he presen, here have been several regime shifs in ineres-rae levels due o he subsanial and susained decline of inflaion and shifs in moneary policy. The purpose of our sudy is no o explain hese shifs bu o allow he daa o provide parameer esimaes of baners responses o ineres-rae changes. 7 In dealing wih daa on a quarerly frequency, we considered he imposiion of he unbiased expecaions hypohesis on ineres-rae changes and he conjoin assumpion of ris-neural pricing o be a second-order consrain for he purposes of his sudy. The focus of his sudy is o esimae baners reacions o prior ineresrae, erm-srucure, and volailiy changes and no o impose a paricular model. The unbiased expecaions hypohesis will be used o help inerpre he esimaed coefficiens, since he pricing ha resuls is ris neural. 16

18 Furhermore, he change in NIM is inversely relaed o he level of prior-period NIM and, since NIM is always posiive, o he rae of change in EA, ceeris paribus. Since he rae of change in EA can be posiive or negaive, is sign mus be accouned for in esimaions. By way of comparison, anoher approach o modeling changes in NIM is o use Io s lemma by assuming ha he change in NIM follows a diffusion process as below: dnim NIM NII NIM NII NIM NIM m m m m 2 dy dr d ij NII y NII r + + σ (7) = 1 = 1 2 i= 1 j= 1 xi x j = 1 where all variables are as described above, x i and x j are ineres raes composed of y and r and saed his way in (7) for simpliciy, and σ ij is he covariance among all ineres-rae changes of asses, dy, and liabiliies, dr. To expand (7), noe ha he erms in parenheses are equivalen o equaion (4), where earning asses are allowed o change. The middle erm in (7) is he drif of NIM over ime and can be hough of as a rend in NIM. When he diffusion process for ineres raes is subsiued from (5) ino (7), he erm in parenheses is equivalen o (6). This approach adds he drif and he second-order sochasic erm wihin he double sum in (7). This final erm can be inerpreed as he porfolio effec on dnim due o ineres-rae volailiy and correlaion a porfolio ris effec. If ineres raes are posiively correlaed wihin mos ineres-rae regimes (see Hanwec and Hanwec [1995]; Hanwec and Shull [1996]), he σ ij are posiive and he sign of he double-sum erm will depend on he sign of he second derivaive of NIM wih respec o ineres raes. This erm could be posiive or negaive depending on wheher he ineres raes are only for asses or only for liabiliies. For asse erms he sign is negaive; for asse and liabiliy erms he sign depends on he weigh of asses and liabiliies a each repricing period and is liely o be negaive for one-year repricing iems; and for all liabiliies he sign is liely o be posiive. Wih posiive correlaions of ineres-rae changes, we expec he weigh of he erms o 17

19 be such ha changes in volailiy will be negaively relaed o he change in NIM for mos bans regardless of produc-line specializaion. This resul is consisen wih he hypohesis expressed in equaion (6), bu wih he correlaions of ineres-rae changes added. Thus, his approach reinforces he role of ineres volailiy for changes in NIM. This form of a model of NIM change is much less heoreically appealing because i assumes ha earning asses and liabiliies are almos exclusively sochasic, similar o he assumpion of Ho and Saunders (1981), when i is well nown ha bans can and do change he disribuion of asses and liabiliies among heir repricing buces subsanially from quarer o quarer for sraegic purposes, presumably o ae advanage of expeced fuure ineres-rae changes (see Saunders and Corne [2003], chap. 9, for his evidence). Thus, we focus our empirical wor using he model represened by (6) while aing advanage of he insighs of he second model regarding ineres-rae volailiy and correlaion by mauriy and ris class. 3.2 Credi Ris Some imporan facors influencing changes in NIM have been lef ou of he models above in order o achieve simpliciy in focusing on ineres-rae change effecs on NIM. One imporan facor, as poined ou by Zarru and Madura (1992), Angbazo (1997), and Wong (1997), is he effec of credi ris or ris of loan losses on NIM. Angbazo and Wong hypohesized ha NIM should be posiively relaed o loan losses, arguing ha greaer credi ris would mean ha bans would charge higher premiums. An implicaion of his hypohesis is ha expeced increases in credi ris would promp bans o raise ineres-rae marups on he basis of hese perceived fuure loan losses. Alhough i may be he case in he long run ha greaer credi ris will lead o higher NIM hrough he pricing of ris, quarerly or shor-run changes in 18

20 he NIM are more liely o respond inversely o increases in credi ris. Lie Zarru and Madura, we argue ha when faced wih higher uncerainy of loan losses ha is, an increase in credi ris of heir porfolios ris-averse ban managers will shif funds o less defaul-risy, lower-yielding asses over he shor-erm horizon. In addiion, ban examiners will pu pressure on bans o reduce heir exposure o risy credis when loan qualiy sars o deeriorae. These supervisory acions imply ha a deerioraion in loan qualiy, indicaed by rising loan losses or nonperforming loans relaive o earning asses, causes bans o lose ineres income from hese loans and move funds o less defaul-risy, lower-yielding asses. Boh effecs end o decrease NIM in he shor run, so ha decreases in credi qualiy end o decrease NIM. We can inegrae hese conceps direcly ino he above model by using equaion (6). The oal change in NIM, dnim, now becomes a funcion of ineres-rae changes and credi-qualiy changes. We can incorporae credi qualiy by defining he value of an earning asse as composed of wo componens: he promised value, less he value of an opion held by he ban (he lender) o ae over he asses of he borrower if he loan is no paid off on ime and in full. 8 An increase in he value of his opion means ha he credi qualiy of he borrower has decreased and he ban s credi ris has increased. This relaionship is shown more formally as EA = BEA P A, BEA, T, Rf ) (8) ( b where EA is he mare value of he earning asse of repricing frequency, BEA is he promised value of he deb, P () is he pu opion on he asses of he firm, A b, T is he ime o repricing, and Rf is he value of he defaul ris-free rae for repricing frequency. Since he 8 See Blac and Cox (1976); Meron (1974); and Cox and Rubensein (1985), for he srucural models for deb valuaion. Concepually, he value of he shareholders ineres can be hough of as a call opion on he asses of he firm, wih he abiliy o pu he asses o he deb holders if he value of he asses is less han he promised value of he deb. Thus deb holders, lenders such as bans, have a shor pu opion on he firm s asses wih a srie price of he promised value of he deb. 19

21 boo value of ineres-earning asses is approximaely equal o he promised value, we can subsiue EA in equaion (6) wih equaion (8) o arrive a he following relaionship: dnim = m = 1 ( BEA NIM (9) P ()) f d( BEA ( BEA ( y, ) + ( BEA P ()) σ dz + y d( BEA p()) L f ( r, ) P ()) P ()) y ( BEA P ()) L σ dz r r dl Since he promised value of he deb is fixed, he value of he pu opion direcly reflecs changes in credi ris. An increase in he value of he pu opion means ha he pu is closer o being in he money and defaul is more liely. By considering hese facors, we see ha he change in NIM is inversely relaed o increases in credi ris. We can evaluae he effec of ineres-rae changes on defaul-risy deb by using equaion (8). An increase in he base ineres-rae index will reduce he promised value, BEA, by increasing he discoun facor. However, a rise in ineres raes will also reduce he value of he pu opion because he presen value of he srie price (he promised value) is reduced. The reducion implies ha defaul-risy deb is less sensiive o a given change in he ineres-rae index han defaul-free deb. If defaul ris is independen of ineres-rae changes, ban specializing in higher credi-ris lending should be less ineres sensiive han bans wih concenraions in defaul-risy deb. 4. Daa and he Empirical Model In his secion we describe he daa, he empirical variables (for ineres-rae shoc, for erm-srucure shoc, for credi shoc, oher insiuional variables, and for seasonaliy), and our empirical specificaions. 20

22 4.1 Daa We obained individual ban daa for he esimaion of hese models from he Repors of Condiion and Income (Call Repors) colleced on a quarerly basis by he FDIC from he firs quarer of 1986 o he second quarer of Daa for financial mare variables are from Haver Analyics and he Federal Reserve Board of Governors. Because of issues relaed o daa consisency and availabiliy, BIF-insured hrifs and Thrif Financial Repor filers are excluded from he sample. Alhough available, ban daa before he firs quarer of 1986 were excluded from he sample because of he exisence of Regulaion Q, which consrained bans abiliy o adjus ineres raes on deposis in response o changes in mare ineres raes. 9 To exclude spurious financial raios, we resriced he sample o commercial bans wih earning asses of $1 million or more and a raio of earning asses o oal asses exceeding 30 percen. This lef 22,077 commercial ban observaions in he sample of bans ha were in exisence for one or more quarers over he sample period. We also excluded any observaion wih missing daa poins, reducing he sample o 17,789 commercial bans. We hen divided he sample ino 12 differen ban groups based on he specializaion and asse size of he ban a he end of each quarer. These ban groups pracically correspond o he classificaion mehod used by he FDIC o idenify a specialy peer group of insured insiuions excep ha we mae hree main aleraions o he FDIC peer grouping o beer reflec differences in he insiuions ris characerisics. Firs, we brea down commercial lenders more finely o beer reflec differences in ris characerisics beween commercial and indusrial (C&I) loan and commercial real esae (CRE) loan porfolios. Second, we separae consider noninernaional bans wih asses over $10 billion o accoun for poenially greaer reliance on hedging aciviies ha may offse he adverse effecs of ineres-rae shocs. Finally, o be able 9 The final phasing ou of Regulaion Q occurred in he second quarer of

23 o compare asse size over ime, we use real asses raher han nominal asses o classify ban size groups. 10 This classificaion mehod helps sraify commercial bans on he basis of heir business models, porfolio composiions, and ris characerisics. Given dissimilariies in heir ris characerisics, we expec bans in hese differen groups o exhibi varying degrees of sensiiviy o credi, ineres-rae, and erm-srucure shocs. We also considered a classificaion mehod based on derivaive aciviies; however, daa on derivaives are severely limied, paricularly for he full sample period, so i would be difficul o assess he exen o which commercial bans use derivaives for hedging purposes. We use asse size as a proxy o idenify groups of bans mos liely o use derivaives o hedge heir ineres-rae ris. The 12 ban groups are Inernaional bans Large noninernaional bans wih real asses over $10 billion Agriculural bans Credi card bans Commercial and indusrial (C&I) loan specialiss Commercial real esae (CRE) specialiss Commercial loan specialiss Morgage specialiss Consumer loan specialiss Oher small specialiss wih real asses of $1 billion or less Nonspecialis bans wih real asses of $1 billion or less Nonspecialis bans wih real asses beween $1 billion and $10 billion. 10 To compue real asses, we divided nominal asses by he CPI-U price-level index for he quarer. 22

24 Because of he size and diversiy of he group of commercial loan specialiss and he grouop of small nonspecialiss, each is furher broen down ino hree groups on he basis of he size of heir real asses. Appendix 1 describes he crieria for each of hese ban groups. Each ban is classified in 1 of he 12 groups in a given quarer, bu i may belong o 2 or more ban groups hroughou he sample period as he ban changes is asse composiion or is business model or boh. For each ban group, we eliminaed any ban ha did no belong o he group for a leas four quarers, hus maing he final sample 16,522 commercial bans. The Call Repors require bans o repor cumulaive year-o-dae income and expenses on a quarerly basis. Reflecing his reporing sandard, mos sudies and quarerly repors by he FDIC and Federal Reserve of ban performance repor NIM as an annualized, cumulaive value (see he FDIC release of he Quarerly Ban Performance Repor a The use of quarerly cumulaive repors ends o smooh changes in NIM, reducing acual quarerly variaions. To overcome his problem, we focus on quarerly changes in he ne ineres margin. For he second quarer hrough he fourh quarer of each year, we esimae acual income and expenses for he quarer by subracing he previous quarer s cumulaive repored values from he curren cumulaive repored values. For he firs quarer, we use repored income and expenses for he quarer. We hen annualize hese values by muliplying each by four. We compared he resuling series wih he cumulaive series in model esimaion and found ha he resuling series performance was much more consisen wih he hypohesized behavior. Therefore, all income and expense derived daa are based on adjused series. The repored earning asses he denominaor of compued raios are he average of ending values for he quarer and he previous quarer. 23

25 Nine panels in figure 1 show rends in ne ineres margins and nonineres income for each of our 12 ban groups. These panels show a long-erm rend of a decline in ne ineres margins for mos ban ypes, beginning around he period. In paricular, inernaional bans have experienced a significan compression in heir ne ineres margins since he early 1990s, wih he median ne ineres margin for he group falling by more han 175 basis poins. I is no clear how much of his long-erm decline can be aribued o he low ineresrae environmen, greaer compeiive pressure, or regulaory changes ha made securiizaion and oher off-balance-shee aciviies more aracive. However, i is ineresing o noe ha he pea year in ne ineres margins roughly corresponds o he implemenaion of capial regulaion rules and promp correcive acion as specified in FDICIA. Aggregae indusry saisics show a growing imporance of nonineres income as a source of ban earnings. The FDIC Quarerly Baning Profile shows ha nonineres income rose from 31 percen of quarerly ne operaing revenue in firs quarer 1995 o 41 percen in second quarer However, mos ban groups did no experience a noable increase in nonineres income as a percenage of average earning asses over mos of he sample period. In fac, he median quarerly nonineres income as a percenage of average earning asses remained mosly sable for mos ban groups hroughou he 1990s. DeYoung and Rice (2004) sugges ha he long-erm increase in nonineres income may have already peaed as he ris-reurn rade-off reached a plaeau. Inernaional bans, large bans wih real asses exceeding $10 billion, and credi card specialiss did experience a sharp increase in nonineres income over he sample period. The median raio of nonineres income o average earning asses for he inernaional ban group rose sharply afer 1997, overaing ne ineres margins as he primary source of his grooup s 24

26 earnings. This rend liely reflecs earnings and produc diversificaion and a greaer reliance on off-balance-shee insrumens by hese bans in response o deregulaion, capial regulaion, and financial mare developmens. 11 Rogers and Siney (1999) found ha bans ha are larger and have smaller ne ineres margins and fewer core deposis, as is he case of inernaional bans, end o engage more heavily in nonradiional aciviies. As figure 1 shows, large bans wih real asses greaer han $10 billion saw heir nonineres income rise seadily, alhough ne ineres income sill represens heir primary source of earnings. The ne ineres margin flucuaed beween 3.5 percen and 4.5 percen of average earning asses for his group of bans. Unlie for oher ban groups, for credi card specialiss he median ne ineres margins did no exhibi a discernible downward rend in he 1990s. The median ne ineres margin for credi card bans increased sharply in he period despie a seady decline in shor-erm ineres raes. A he same ime, he median nonineres income for he group has risen sharply since This rend liely reflecs a widespread use of ris-based pricing and ris-relaed fees in response o heighened rae compeiion and greaer availabiliy of credi card loans o higher-ris and higher-revenue-generaing borrowers han previously. 12 Figure 2 presens he median quarerly reurn on average earning asses (ROA) for seleced groups of bans. The median ROA for large and midier bans has improved significanly since he implemenaion of FDICIA, and i has remained more sable since hen compared wih prior periods. Beween 2002 and 2003, however, large bans wih real asses greaer han $10 billion saw heir ROA rising sharply, whereas inernaional and midier 11 See Angbazo (1997) for he effecs of off-balance-shee insrumens on ne ineres margins. Angbazo found a negaive relaionship beween leers of credi, ne securiies len, and ne accepances acquired and ne ineres margins, bu a posiive relaionship beween ne loans originaed/sold and ne ineres margins. 12 See Furlei (2003) for discussions of recen developmens in credi card pricing and fee income. 25

27 nonspecialiss repored weaer earnings. These differing rends sugges diversiy across hese hree larges asse size groups in heir business models in erms of asse composiion, correlaion among earning componens, and earnings managemen. The earnings volailiy of inernaional bans suggess ha hey are vulnerable o mare facors oher han hose included in our model; however, discussion on he effec of hese facors on ban earnings is ouside he scope of his paper. As for large bans, he median ROA for small nonspecialis bans made discree improvemens in The ROA of hese bans, paricularly he smalles asse size group, has exhibied a high degree of seasonaliy over ime. 4.2 Empirical Variables Appendix 2 liss he explanaory variables included in our empirical model and heir expeced signs. All variables represening financial raios or ineres raes are expressed in annualized percenage erms. Ban-specific variables and financial mare variables included in he empirical model are derived from he heoreical model of ban behavior presened in secion 3 of his paper. Table 1 presens descripive saisics for ban-specific variables for each ban group. To preserve earnings daa for an individual insiuion a a given ime, we did no adjus he ban daa for mergers and acquisiions ha occurred over he sample period. Insead, we screened he sample for any aberran daa on an individual-ban basis. As discussed below, here exis significan variaions in he value of each of hese ban-specific variables across ban groups as well as wihin he given ban group Ineres-Rae-Shoc Variables 26

28 VOL_1Y represens shor-erm ineres-rae volailiy and is measured by he sandard deviaion of a weely series of one-year Treasury yields for he quarer. ST_DUMMY is a dummy variable ha aes a value of one if he one-year Treasury yield rose during he quarer, and zero if he yield fell. Figure 4 illusraes a mosly posiive bu imperfec correlaion beween he quarerly shor-erm ineres-rae volailiy and he level of shor-erm ineres raes. Equaion (7) posis ha he coefficiens for boh VOL_1Y and ST_DUMMY would have a negaive sign for mos bans. The duraion gap beween asses and liabiliies measures respecive changes in asses and liabiliies due o an ineres-rae shoc and is a ey deerminan of ban ne ineres margins (Mays [1999]). The duraion gap reflecs he repricing frequency of asses and liabiliies as well as he value of embedded call opions. Daa necessary o calculae he duraion gap are no colleced in he Call Repor for commercial bans, so we are prevened from using a repored duraion gap in our empirical model. As a proxy for he ineres-rae sensiiviy of ban porfolios, we use ne shor-erm asses he difference beween shor-erm asses and shor-erm liabiliies. We define a repricing frequency less han one year as shor erm. STGAP_RAT is ne shor-erm asses as a percenage of earning asses. Alhough here have been changes in Call Repor daa iems and heir definiions over ime, we believe ha STGAP_RAT is generally comparable over ime because many of hese changes affeced boh asses and liabiliies. Our definiion of STGAP_RAT includes nonmauring liabiliies ha are discussed more fully below. Table 1 shows ha, whereas inernaional bans and credi card specialiss end o have beer mached asses and liabiliies han oher ban groups, consumer loan specialiss, morgage specialiss, oher small specialiss, and small nonspecialis bans end o have he mos unmached balance shees. Holding everyhing else consan, we expec he coefficien for 27

29 STGAP_RAT o have a negaive sign since longer-erm asses have higher yields han shorererm asses wih he same ris characerisics. In addiion, we expec he size of STGAP_RAT o have a posiive effec on NIM when shor-erm ineres raes rise. Flannery and James (1984) show ha deposis wih uncerain mauriy, such as demand deposis, regular savings accouns, and small ime deposis, have an effecive mauriy longer han one year. This finding suggess ha he effecive cos of hese liabiliies is relaively insensiive o changes in mare ineres raes. Indeed, Mays (1999) found ha hrifs wih a high percenage of nonmauring deposis, defined as he sum of demand deposis and regular savings, experienced a posiive increase in ne ineres margins in response o a posiive ineres-rae shoc. Alhough hese relaionships may have changed in recen years as shor-erm ineres raes have reached 1.0 percen and less, we can es for any changes in his srucure wih models esimaed for differen periods. We include NM_RAT, nonmauring deposis as a percenage of earning asses, in he model o proxy for he degree of ineres-rae sensiiviy of he ban s funding from nonmauring deposis. As shown in able 1, commercial loan specialiss and small nonspecialis bans seem o rely mos heavily on nonmauring deposis o fund heir lending, whereas inernaional and credi card bans fund heir lending aciviies wih more ineres-raesensiive liabiliies. On he basis of previous sudies, we expec he coefficien for NM_RAT o have a posiive sign. In addiion, we expec he size of NM_RAT o have a marginal and posiive effec on NIM as ineres raes rise, given he documened insensiiviy of nonmauring liabiliies o ineres rae changes (Mays [1999]) Term-Srucure-Shoc Variables 28