Banks as Patient Fixed-Income Investors *

Transcription

1 Banks as Patent Fxed-Income Investors * Samuel G. Hanson, Andre Shlefer, Jeremy C. Sten, and Robert W. Vshny Frst draft: February 2014 Ths draft: January 2015 Abstract We examne the busness model of tradtonal commercal banks when they compete wth shadow banks. Whle both types of ntermedares create safe money-lke clams, they go about ths n dfferent ways. Tradtonal banks create safe clams by holdng llqud fxedncome assets to maturty, and they rely on depost nsurance and costly equty captal to support ths strategy. Ths strategy allows bank depostors to reman sleepy : they do not have to pay attenton to transent fluctuatons n the market value of bank assets. In contrast, shadow banks create safe clams by gvng ther nvestors an early ext opton requrng the rapd lqudaton of assets. Thus tradtonal banks have a stable source of fundng, whle shadow banks are subject to runs and fre-sale losses. In equlbrum, tradtonal banks have a comparatve advantage at holdng fxed-ncome assets that have only modest fundamental rsk, but are llqud and have substantal transtory prce volatlty, whereas shadow banks tend to hold relatvely lqud assets. * Hanson, Shlefer and Sten are from Harvard Unversty, and Vshny s from the Unversty of Chcago. We are grateful to semnar partcpants at the 2014 NBER Sprng Corporate Fnance Meetng, the 2014 NBER Macro, Money and Fnancal Frctons Summer Insttute, the Federal Reserve Bank of San Francsco, Harvard Unversty, NYU Stern, UC Berkeley Haas, and USC Marshall for helpful comments, as well as to Malcolm Baker, John Campbell, Eduardo Dávla, Harry DeAngelo, Doug Damond, Mhr Desa, Gary Gorton, Robn Greenwood, Bengt Holmstrom, Arvnd Krshnamurthy, Davd Scharfsten, René Stulz, Ad Sunderam, Paul Tucker, Annette Vssng- Jorgensen, and Yao Zeng for valuable suggestons. We also thank Yueran Ma for excellent research assstance.

2 I. Introducton What defnes the busness model of tradtonal banks n a modern fnancal system where they compete wth market-based ntermedares such as shadow banks? To address ths queston, we present a model n whch tradtonal and shadow banks co-exst n the marketplace. We begn wth the premse that the prmary functon of both types of ntermedares s to create safe, moneylke clams that are of value to households because they are useful for transactons purposes (Gorton and Pennacch 1990, Sten 2012, DeAngelo and Stulz 2014). However, tradtonal banks and shadow banks nvest n dfferent portfolos of assets to support such clams. Tradtonal banks hold llqud fxed-ncome assets, such as long-term securtes and loans, whch may be subject to substantal prce fluctuatons but are relatvely safe n the long run. To hold such assets, they mantan a costly equty cushon n ther captal structure, but also rely on depost nsurance and other elements of the government safety net. Ths strategy allows bank depostors to reman sleepy : they do not have to pay attenton to transent fluctuatons n the mark-to-market value of bank assets and never run. In contrast, the shadow-bankng system ntermedaton chans that often nvolve money-market funds reles less on the government safety net and costly equty captal. For shadow banks, manufacturng money-lke clams requres them to hold more n the way of relatvely lqud assets that can be easly sold at only a modest dscount should ther nvestors decde to ext. We see asset fre sales as a key source of llqudty. In our model, asset lqudatons temporarly push prces below fundamental value. So, on the one hand, tradtonal banks more stable depost fundng structure has an advantage: t enables them to hold nvestments to maturty, rdng out transtory valuaton shocks untl prces revert to fundamental values. On the other hand, fundng stablty s expensve due to hgher costs of equty captal and regulatory complance. Because the endogenous fre-sale dscount s greater when shadow banks hold more of an asset, ths tradeoff pns down the equlbrum holdngs of any gven asset across ntermedary types. The most lqud assets are held entrely by shadow banks, whle the less lqud (but stll fundamentally safe) assets are held entrely by commercal banks. When an asset s held by both ntermedary types, the relatve holdngs of banks and shadow banks must be such that the expected loss to a shadow bank from lqudatng an asset at a temporary dscount to fundamental value s just balanced by the added cost a tradtonal bank pays for more stable fundng. Ths logc leads to our man fndng: for tradtonal banks there s a crtcal synergy between the asset and lablty sdes of the balance sheet. Issung stable money-lke clams s complementary 1

3 wth nvestng n fxed-ncome assets that have only modest fundamental rsk, but are relatvely llqud and may have substantal exposure to nterm fre-sale rsk and the accompanyng transtory prce volatlty. In our vew, ths synergy between fundng structure and asset choce s at the heart of the modern busness of commercal bankng, and s what fundamentally dstngushes tradtonal banks from shadow banks: tradtonal banks are patent nvestors that can nvest n llqud fxedncome assets wth lttle rsk of beng nterrupted before maturty. Whle our formal model emphaszes fre sales (Shlefer and Vshny 1992), our message would also emerge n other models n whch early lqudaton can occur at prces below fundamental value. For example, early lqudaton can be costly n models that combne nose trader shocks wth lmted arbtrageur rsk-bearng capacty (DeLong et al 1990, Shlefer and Vshny 1997). Alternatvely, lqudaton costs could come from adverse selecton (Gorton and Pennacch 1990, Dang, Holmstrom, and Gorton 2013). The general pont s that transtory non-fundamental movements n asset prces are central to understandng fnancal ntermedaton, and especally the connecton between the asset and lablty sdes of ntermedary balance sheets. A stable fundng structure s an mportant source of comparatve advantage for holdng assets that are vulnerable to transtory prce movements. In ths regard, tradtonal banks are smlar to deep-pocketed arbtrageurs who specalze n fxed-ncome assets. It s mportant to stress that what our model actually pns down s not lterally the roles of dfferent types of legal nsttutons (e.g., commercal banks or money market funds), but rather the equlbrum mx between two ntermedaton strateges that use rsky assets to back money-lke clams. For any gven asset, our model asks how much of ts total supply wll be ntermedated usng a stable fundng strategy that reles on an equty cushon and nsured deposts, and how much usng an unstable fundng strategy where nvestors protect the safety of ther clams wth an early ext opton. The nterdependences between asset characterstcs and fundng strateges are the true equlbrum outcomes of our model. Of course, n realty there can be a close correspondence between fundng strateges and specfc legal forms. In partcular, when ntermedares are dstngushed by ther access to depost nsurance and the lender of last resort, commercal banks are the domnant nsttutonal vehcle for mplementng the stable fundng strategy. And we prmarly assocate the unstable fundng strategy wth the so-called shadow bankng system. We motvate our analyss n Secton II by presentng some stylzed facts about the assets and labltes of modern commercal banks. We show that banks have sgnfcant holdngs of relatvely llqud long-term fxed-ncome securtes, such as asset-backed securtes, mortgage-backed 2

4 securtes, and corporate bonds. At the same tme, banks generally avod the most lqud debt securtes, such as short-term money-market paper and Treasures, as well as hghly rsky securtes such as equtes. We vew these facts as mportant clues for understandng the busness of commercal bankng. In Secton III, we present our model of alternatve strateges for supportng money-lke clams, and show how commercal and shadow banks coexst n equlbrum. We then turn to some evdence bearng on our model s key predctons about the connectons between the asset and lablty sdes of ntermedary balance sheets. Secton IV brefly takes a hstorcal look at the U.S. commercal bankng ndustry. We fnd that pror to the ntroducton of federal depost nsurance, U.S. commercal banks followed a strategy that resembles that of shadow banks today. Lke today, a commercal bank n, say, 1870 was n the busness of takng deposts and thereby offerng ts customers safe money-lke clams. At the same tme, commercal banks n 1870 held assets wth much shorter maturtes, and experenced more runs, than they do today. The shft of commercal bank assets to longer-maturty loans and long-term securtes can be lnked to the ntroducton of depost nsurance, as our model predcts. Another way to examne the predctons of the model s to look at the asset and lablty structures of fnancal nsttutons more broadly. In Secton V, we use the Fnancal Accounts of the Unted States (formerly the Flow of Funds) to provde some contemporary aggregate evdence addressng the model s key predctons. In the data, lookng across fxed ncome asset classes, today s tradtonal banks have a larger market share n more llqud assets, be they loans or securtes. Smlarly, lookng across fnancal ntermedary types, ntermedares wth more stable fundng such as tradtonal banks have asset portfolos that are more llqud. In ths way, our model yelds a novel synthess of several aggregate facts about the structure of fnancal ntermedaton. Our paper relates to several strands n the lterature. Our startng pont s the lablty-centrc vew of banks, whch holds that an mportant part of banks value comes from ther ablty to manufacture safe labltes. 1 Ths vew helps make sense of the fact that, n contrast to nonfnancal frms, banks have captal structures that are hghly homogenous n both the cross secton and the tme seres: they are almost always heavly depost-fnanced. At the same tme, ths lablty-centrc 1 Ths vew has ts roots n Gorton and Pennacch (1990). Recent papers n ths ven nclude Dang, Gorton and Holmstrom (2013), DeAngelo and Stulz (2014), Gennaol et al (2013), Gorton and Ordonez (2014), Sten (2012), and Krshnamurthy and Vssng-Jorgensen (2013). 3

5 vew does not explan why banks hold llqud loans and securtes. 2 To the contrary, the labltycentrc vew has led some observers to advocate narrow bankng, whereby bank-created money s backed entrely by safe lqud assets, such as Treasury blls (see Pennacch 2012). As a postve descrpton of commercal bankng, narrow bankng s very far from what we observe n the world, and s unlkely to break even. The challenge s to understand why banks smultaneously fnance themselves wth deposts and hold long-term and llqud fxed-ncome assets. A second group of theores explctly addresses the queston of what tes together the asset and lablty sdes of bank balance sheets.e., why s t that the same nsttutons that create prvate money choose to back ther safe clams not by nvestng n T-blls, but rather by nvestng n loans and other relatvely llqud assets? What s the synergy between the two actvtes? In a classc contrbuton, Damond and Dybvg (1983) argue that banks allow households who are unsure of the tmng of ther consumpton needs to more effcently nvest n long-lved projects whch are costly to nterrupt early. 3 Damond and Dybvg emphasze depost nsurance as the source of stablty that keeps depostors sleepy and prevents runs. We use ths observaton to address a queston not taken up by Damond and Dybvg: what types of assets s t optmal for depost-nsured banks to hold? Several other studes have focused on potental complementartes between banks assets and labltes. Damond and Rajan (2001) suggest that the fraglty of runnable bank deposts dscplnes bank management, enhancng the value of llqud bank loans. Kashyap, Rajan, and Sten (2002) hghlght the smlartes between demand deposts and loan commtments, and the ablty of an nsttuton that offer both products to economze on costly lqudty buffers; Gatev and Strahan (2006) provde supportng evdence for ths vew. Gennaol, Shlefer, and Vshny (2013) also argue that a central functon of banks s to provde safe clams, but focus on asset-sde dversfcaton and tranchng as technologes for backng such safe labltes. Relatedly, DeAngelo and Stulz (2014) emphasze dversfcaton and rsk management strateges to reduce the rskness of bank assets. Our work also connects wth several other themes. Frst, a number of papers explore the jont roles of banks and securtes markets n allocatng credt and satsfyng the demand for lqudty (Holmstrom and Trole 1997; Damond 1997). Second, several papers study the shadow bankng system and ts role n the fnancal crss (Brunnermeer and Pedersen 2009; Coval, Jurek, 2 Asset-centrc theores of bankng, such as those that see banks as delegated montors (Damond 1984), do not draw a dstncton between banks and other non-bank lenders, whch we see as crtcal. 3 Taken lterally, the Damond-Dybvg model does not admt a ratonale for banks to hold marketable securtes; see Jackln (1987). Taken less lterally, the model makes no predctons on the knds of assets banks would hold. 4

6 and Stafford 2009a and 2009b; Shlefer and Vshny 2010; Gorton and Metrck 2010 and 2011; Damond and Rajan 2011; Shn 2009; Sten 2012; Gennaol, Shlefer, and Vshny 2012 and 2013; Kacperzcyk and Schnabl 2013; Krshnamurthy, Nagel, and Orlov 2013; Chernenko and Sunderam 2013; Sunderam 2014; Weymuller 2013, Morera and Savov 2014). Fnally, a few recent papers measure the msmatch between the lqudty of ntermedary assets and labltes (Brunnermeer, Gorton, and Krshnamurthy 2011 and 2013 and Ba, Krshnamurthy, and Weymuller 2013). II. Motvatng Evdence A. Fact 1: Bank labltes are hghly homogeneous Banks lablty structures are hghly homogeneous: banks are almost always fnanced largely wth deposts. Ths fndng holds both n the cross-secton and over tme. In the crosssecton, Table I shows varous balance sheet tems as a share of total assets at the end of 2012 for US commercal banks. To assess the cross-sectonal heterogenety n balance sheets, we show the value-weghted average share, the 90 th percentle, and the 10 th percentle for each tem. To avod the dosyncrases assocated wth the smallest banks, we focus on banks wth assets greater than $1 bllon. Table I reveals a hgh degree of homogenety n the amount of depost fundng. The average bank fnances 76% of ts assets wth deposts. A bank at the 90 th percentle n terms of the dstrbuton s 89% depost-fnanced, only a bt more than a bank at the 10 th percentle whch s 74% depost-fnanced. A smlar pattern holds n the tme seres for the bankng ndustry as a whole. Fgure 1 shows the evoluton of the aggregate balance sheets of US banks from 1896 to As shown n Panel A, banks lablty structures have been very stable over the past 115 years. Deposts have fnanced 80% of bank assets on average wth an annual standard devaton of just 8%. These patterns are n sharp contrast to those for non-fnancal frms, where captal structure tends to be far less determnate, both wthn ndustres and over tme. Ths suggests that for banks unlke non-fnancals, and counter to the sprt of Modglan and Mller (1958) an mportant part of ther economc value creaton takes place on the lablty sde of the balance sheet, va deposttakng. Ths s broadly consstent wth the lterature that has followed Gorton and Pennacch (1990). B. Fact 2: Bank assets are more heterogeneous There s consderably more heterogenety on the asset sde of bank balance sheets, and n partcular n ther mx of loans and securtes. In the 2012 cross-secton, a bank at the 10 th percentle of the dstrbuton had a rato of securtes to assets of 6.9%, whle for a bank at the 90 th percentle 5

7 the rato was almost sx tmes hgher, at 40.7%. 4 One nterpretaton of ths heterogenety s as follows: whle lendng s obvously very mportant for a majorty of banks, a bank s scale need not be pnned down by the nature of ts lendng opportuntes. Rather, n some cases, t seems that a bank s sze s determned by ts depost franchse, and that takng deposts as gven, ts problem becomes one of how to best nvest them. Agan, ths lablty-centrc perspectve s very dfferent from how we are used to thnkng about non-fnancal frms, whose scale s almost always presumed to be drven by ther opportuntes on the asset sde of the balance sheet. C. Fact 3: Bank securtes portfolos do not seem to be precautonary lqudty buffers Whle banks are qute heterogeneous n ther loan and securtes mx, wthn the category of securtes banks appear to have relatvely well-defned preferences. As can be seen n Table I and Panel A of Fgure 2, banks hold very lttle n the way of Treasury and agency securtes: these two categores accounted for just 7.7% and 5.8% of total securtes holdngs on a value-weghted bass n The bulk of ther holdngs are n agency mortgage-backed securtes (MBS) and other types of mortgage-lnked securtes such as collateralzed mortgage oblgatons (CMOs) and commercal mortgage-backed securtes (CMBS): these collectvely accounted for 57.7% of securtes holdngs n Also mportant s the other category, whch ncludes corporate and muncpal bonds, as well as asset-backed securtes, and whch accounted for 29.3% of holdngs n Ths composton of banks securtes portfolos s not what one would expect f banks were smply holdng securtes as a hghly lqud buffer stock aganst unexpected depost outflows or loan commtment drawdowns. It also appears superfcally, at least at odds wth the narrow-bankng premse that one can proftably explot a depost franchse smply by takng deposts and parkng them n T-blls. Rather, t looks as f banks are purposefully takng on some mx of duraton, credt and prepayment exposure n order to earn a spread relatve to T-blls. And ndeed, over the perod 1984 to 2012, the average spread on banks securtes portfolo relatve to blls s 1.73%. In ths ven, t s nterestng to ask how proftable banks would be n a counterfactual world n whch ther depost-takng behavor was exactly the same, but nstead of allocatng ther securtes holdngs as they actually do, they followed a narrow-bankng strategy of nvestng only n T-blls. The proftablty of a narrow bank that takes deposts DEP at a rate and nvests them n T-blls payng R F, whle ncurrng depost-related nonnterest expenses of NONINTEXP (e.g., 4 These fgures on securtes holdngs do not nclude banks holdngs of cash and reverse repo, whch averaged 10.2% and 4.1% of assets on a value-weghted bass n

8 employee salares, brcks-and-mortar expenses assocated wth bank branches, and other operatng expenses), and earnng depost-related nonnterest ncome of NONINTINC (e.g., servces charges on depost accounts) s gven by NONINTINC NONINTEXP R F RDEP. DEP DEP (1) We carry out ths calculaton for the aggregate commercal bankng ndustry from To compute the gross depost spread, R F R DEP, we use the rate on 3-month Treasury blls as our proxy for R F and compute R DEP from Call Reports as the nterest pad on deposts dvded by deposts. Depost rates appear to embed a sgnfcant convenence premum relatve to short-term market rates, as the gross depost spread averages 0.87% over our 29 year sample. We next add the nonnterest ncome that banks earn from servce charges on depost accounts from Call Reports. Ths averages 0.49% of deposts over our sample. Fnally, we subtract the non-nterest expense assocated wth depost-takng. Ths s not drectly avalable from Call Reports: banks report ther total nonnterest expense, but we are only nterested n that porton attrbutable to depost-takng. 5 As detaled n the Appendx, we use a hedonc-regresson approach to nfer the expenses assocated wth depost-takng. Although these expenses have trended down due to advances n nformaton technology, they reman substantal, averagng 1.30% of deposts over the past 29 years. Combnng these peces as n equaton (1), we estmate the average proftablty of narrow bankng between 1984 and 2012 to be 0.06% of deposts (0.06% = 0.87% % 1.30%). 6 In other words, the nterest rate dfferental between deposts and short-term marketable rates and the assocated fee ncome s largely offset by the drect costs of operatng a depost-takng franchse. Gven these numbers, t s perhaps not surprsng that banks choose to nvest n rsker securtes that earn a spread relatve to T-blls. Of course, the large costs of depost-takng that we document ultmately represent an endogenous choce for tradtonal banks, and so must be explaned as an equlbrum outcome n any fully satsfactory model. For example, banks could always choose to hold down costs by offerng fewer physcal branch servces to ther customers, smlarly to moneymarket mutual funds. We return to the endogenety of depost-takng expenses below. 5 In 2012, banks had non-nterest operatng expenses equal to 2.96% of total assets. These can be decomposed nto wage and salary expenses of 1.32%, buldng occupancy expenses of 0.32%, and other expenses of 1.32%. 6 Ths 0.06% fgure s probably an upper bound on the proftablty of narrow bankng. As explaned n the Appendx, our methodology for attrbutng bank expenses to dfferent actvtes leaves an unallocated cost, whch can be thought of as fxed overhead. Ths overhead cost averages 0.63% of deposts from If 50% of ths amount s allocated back to depost-takng, the estmated proftablty of narrow bankng drops to -0.25%. 7

9 D. Dscusson Our synthess of these stylzed facts s that tradtonal banks are n the busness of takng deposts and nvestng these deposts n fxed-ncome assets that have certan well-defned rsk and lqudty attrbutes, but whch can be ether loans or securtes. The nformaton-ntensve nature of tradtonal lendng n the Damond (1984) delegated montorng sense whle clearly mportant n many cases, may not be the defnng feature of bankng. Rather, the defnng feature may be that, whether they are nformaton-ntensve loans, or relatvely transparent securtes, banks seek to nvest n fxed-ncome assets that have some degree of prce volatlty and llqudty, and so offer a hgher return than very lqud and safe Treasury securtes. In ths sense, small busness loans, assetbacked securtes, and CMOs are on one sde of the fence, and Treasures on the other. Before proceedng, we should address a natural frst reacton to ths nterpretaton. Perhaps banks propensty to nvest n rsky securtes merely reflects the fact that they are takng advantage of the put opton created by depost nsurance. The evdence we have assembled on the patterns of banks securtes holdngs may just reflect a moral hazard problem, and nothng more. One way to address ths hypothess s to redo the analyss n Panel A of Fgure 2, restrctng the sample to those banks wth the hghest levels of captal at any pont n tme those above the medan of the dstrbuton by the rato of equty to assets. Ths s done n Panel B of Fgure 2. The basc patterns for hghly captalzed banks n Panel B are very smlar to those n Panel A for all banks. Gven that these hghly captalzed banks are less lkely to mpose losses on the depostnsurance fund, we suspect that there s somethng deeper here than can be explaned by a smple appeal to depost-nsurance-nduced moral hazard. III. Model We develop a smple model n whch banks and shadow banks compete as buyers of assets wth dfferent degrees of fundamental and lqudty rsk. By rasng expensve equty captal and ganng access to government depost nsurance, tradtonal banks obtan stable fundng and are able to avod asset fre sales. As a result, tradtonal banks can create money-lke clams by patently nvestng n llqud fxed-ncome assets, whch are safe n the long run but vulnerable to short-term prce volatlty. Shadow banks have less expensve fundng, but are vulnerable to runs and early asset lqudatons. Whle ther relance on early ext means that shadow banks can create money-lke clams by nvestng n assets wth hgher fundamental rsk, these assets must be more lqud. 8

10 Although we use the terms tradtonal bank and shadow bank as a short-hand, we emphasze that the model speaks to ntermedaton strateges as opposed to specfc legal nsttutons. A. Settng The basc structure of the model s smlar to Sten (2012). The model has three dates, t = 0, 1 and 2. There are N long-lved rsky assets ndexed by = 1, 2,, N. Asset s avalable n a fxed supply of Q. For smplcty, we assume that the payoffs on these assets are perfectly correlated, and assets only dffer n the magntudes of these payoffs n the bad state of the world. The ndvdual assets n our model mght correspond to corporate loans, mortgages, mortgage-backed securtes (MBS), US Treasures, or even equtes. The model features three types of actors: households, tradtonal banks, and shadow banks. Households do not drectly own any of the rsky assets. Instead, households nvest n safe and rsky clams ssued by tradtonal and shadow banks, whch n turn back these clams by holdng the underlyng rsky assets. Intermedaton s effcent here because households are wllng to pay a premum for completely safe clams, and some form of ntermedaton s requred to create safety none of the prmtve assets are themselves safe. Outsde of ths demand for safe money-lke clams, households are assumed to be rsk neutral. In other words, once a clam has any rsk at all, the dscount rate appled by households s fxed at a dscretely hgher level. Ths corresponds to the followng household utlty functon, taken from Sten (2012) U C E[ C ] M, (2) 0 2 where the notatonal conventon s that a household has M dollars of money-lke clams f t has clams that are guaranteed to pay off an amount M at t = 2. The dscount factor appled to all rsky clams s thus 1 whle the dscount factor appled to safe, money-lke clams s + where 0. The former follows from the observaton that a household s ndfferent between havng unts of tme-0 consumpton and a rsky clam that delvers one unt of tme-2 consumpton n expectaton. The latter follows from the fact that a household s ndfferent between havng + unts of tme-0 consumpton and a rskless clam that always delvers one unt of tme-2 consumpton. Such a clam delvers unts of utlty from expected future consumpton, along wth addtonal unts of utlty n current monetary servces. When > 0, the dscount rate appled to safe, money-lke clams, 1/(+ ), s less than the dscount rate appled to rsky clams, 1/. As n Sten (2012), Gennaol et al. (2013), and DeAngelo 9

11 and Stulz (2014), the assumptons of the Modglan-Mller (1958) theorem no longer hold and the value of a rsky asset may depend on the way t s fnanced usng safe and rsky clams. 7 The tmng of the model s as follows. Each rsky asset pays R at t = 2 f the aggregate economc state of the world s good, but a lower amount z < R f the aggregate economc state at t = 2 s bad. In addton, there s a very small probablty of an economc dsaster n whch case all rsky assets pay 0. At tme 1, there s an nterm news event about the future economc state. Wth probablty p, the nterm news s optmstc, whch means that the aggregate state wll be good at tme 2 and all assets wll defntely pay R. Wth probablty (1 p), the news s pessmstc, whch means that there s a subsequent probablty of of the dsaster state n whch there s a zero payoff on all rsky assets at tme 2 and a (1 q ) probablty of the bad state and low payoff on all assets. Thus, after pessmstc news at tme 1, the fundamental value of asset s F = qr + (1 q )z. Tme t = 0 Intermedares purchase the rsky asset and ssue safe and rsky clams to households Tme t = 1 Pessmstc news arrves wth probablty 1 p. Shadow banks must sell at a dscount, k. Tradtonal banks are able to hold to maturty. Tme t = 2 Payoff on rsky asset revealed. Payoff on clams ssued to households also revealed. p Optmstc news q R Good state 1 p Pessmstc news Fundamental value after pessmstc news at t=1 s F = qr + (1 q )z. However, the market prce s only k F F. 1 q z 0 Bad state Dsaster state The small probablty of an economc dsaster the exstence of tal rsk means that t s mpossble to rase unnsured fundng that s both stable and completely safe. In other words, ntermedares can only manufacture safe clams by ether relyng on an early ext opton, n whch case the resultng fundng s unstable, or on depost nsurance, n whch case t s stable. Thus, our 7 The assumpton that all money-lke clams are perfect substtutes s a smplfcaton. Krshnamurthy and Vssng- Jorgensen (2013) and Sunderam (2014) explore mperfect substtutablty between dfferent money-lke clams. 10

12 assumpton that > 0 s a smple way of capturng the robust fact that ntermedares who rely heavly on short-term, unnsured fundng have always been vulnerable to run-lke wthdrawals when bad news arrves. Of course, f = 0, t would be possble to rase stable, fundng wthout depost nsurance, smply by lmtng the amount of short-term clams to the worst-case payoff, z. And, ndeed, all of our formal results carry through n the specal case where = 0. However, n ths case, the quantty of stable deposts would be lmted by asset payoffs n the worst possble scenaro. Our central assumpton deals wth the dfference between the fundamental value of asset at tme 1, and ts market value. We assume that, f there s pessmstc news at tme 1, the market value of asset s k F F. When k < 1, ths market prce reflects a fre-sale dscount to fundamental value. The value of k s endogenous and asset-specfc and depends on the equlbrum quantty of asset that s lqudated at tme 1. We return to ths feature momentarly. Because our model only features aggregate rsk and the payoffs on all assets are perfectly correlated, we are abstractng away from the need for dversfcaton and rsk management whch DeAngelo and Stulz (2014) argue are central to ntermedares ablty to produce safe money-lke clams. Our approach can be thought of as reflectng the dea that ntermedares have already done the best they can on these dversfcaton and rsk-management fronts, leavng only aggregate rsk that cannot be dversfed away or hedged. B. Intermedaton strateges To examne the dfferent ways the rsky assets can be held and used as backng to create safe clams, we consder two ntermedaton strateges: stable tradtonal bankng and unstable shadow bankng. At t = 0, households can nvest n ether tradtonal or shadow bank deposts, both of whch are completely safe and are valued at + per dollar pad at t = 2. Alternatvely, households can buy bank equty or shadow bank equty, both of whch are rsky and are valued at per dollar pad n expectaton at t = 2. Fracton of rsky asset s purchased by shadow banks at t = 0 and fracton 1 s purchased by tradtonal banks. We examne how the equlbrum market shares of the tradtonal and shadow bankng strateges vary as we change the propertes of the asset n queston. B.1. Tradtonal bankng The tradtonal bankng strategy uses depost nsurance and a hold-to-maturty nvestment approach to back safe short-term clams. A combnaton of rsk-based captal requrements and farly prced depost nsurance prevents tradtonal banks from explotng the depost nsurance fund. Specfcally, we assume that the government offers tradtonal banks actuarally far depost 11

13 nsurance that pays off n the dsaster state. Wth a small probablty of an economc dsaster, tradtonal banks hold-to-maturty strategy can only be used to create safe clams f t s combned wth depost nsurance. To protect taxpayers from further exposure, the government mposes a partcular form of rsk-based captal regulaton: the bank s requred to hold enough captal aganst any asset such that the depost nsurer never suffers losses n equlbrum n the bad (as opposed to the dsaster) state. Snce the bank plans to always hold the rsky asset to maturty, the maxmum amount of nsured money-lke clams that can be created usng asset under ths regulatory regme s z, whch s the payoff n the bad state at tme 2. To satsfy the rsk-based captal rule, the remander of the asset purchase must be fnanced by rsky equty captal whch s more expensve. Snce the dsaster state occurs wth probablty (1 p) and depost nsurance pays z n ths state, the actuarally far nsurance premum dscounted back to tme 0 s (1 p)z. In the lteral context of the model, captal regulaton and the depost nsurance premum are the only costs to beng a depost-nsured bank wth stable fundng, as opposed to a shadow bank wth unstable fundng. More broadly, however, one mght nterpret what we are callng the cost of equty captal as encompassng a varety of other costs that go along wth beng a tradtonal bank. These nclude the costs of other types of regulaton, as well as the brcks-and-mortar costs of settng up the sort of branch network that attracts retal depostors. The total value of clams the bank can ssue at tme 0 usng the rsky asset as backng s Value of bank deposts Insurance premum Value of bank equty B V ( ) z (1 p) z ( p(1 p) q)( Rz ) Money premum Expected cash flows z [ pr(1 p) F]. where, agan, F = qr + (1 q )z s the fundamental value of asset followng pessmstc news at tme 1. In any equlbrum where banks hold asset, banks zero proft condton ensures that the market value of asset equals B V. Because households are wllng to pay a premum for absolutely safe clams, equaton (3) shows that the total value of clams ssued by banks exceeds the expected cash flows on the rsky asset dscounted at the rsky rate: banks capture a money premum of z because depost nsurance enables them to use the rsky asset to back z unts of safe clams. B.2. Shadow bankng An alternatve ntermedaton strategy for creatng safe money-lke clams s shadow bankng. In the real world, what we are callng the shadow bankng strategy often nvolves a chan of market-based transactons whch can nvolve several dstnct legal nsttutons. 12 (3)

14 Perhaps the smplest of these nsttutons s a money market fund (MMF) that nvests n assets that are completely rskless such as Treasury blls and ssues what are effectvely deposts to households. Thngs become more complex when the asset ultmately backng the MMF deposts s not completely rsk-free. To ensure that the MMF deposts are truly safe, some nsttuton along the ntermedaton chan must contrbute fnancng n the form of equty captal. At the end of the chan, households own a combnaton of money-lke MMF deposts and hghly-levered equty. Ths shadow bankng strategy can be mplemented usng several alternatve nsttutonal arrangements, wth more or fewer lnks n the chan. For example, a mortgage-backed securty (MBS) may ultmately wnd up backng money-lke clams n several ways: A broker-dealer afflate of a unversal commercal bank fnances the MBS usng ts own equty and a short-term repurchase agreement wth a money market fund. A hedge fund acqures the MBS usng ts own equty and an overnght collateralzed loan a blateral repo from ts prme broker. The prme broker n turn uses the same collateral to borrow from a money fund n the tr-party repo market, a process called rehypothecaton. A structured nvestment vehcle fnances the MBS usng ts own equty and asset-backed commercal paper that s then sold to a money market fund or an nsttutonal cash manager. In each case, the common denomnator s that there s a short-term clam at the end of the chan that s flghty.e., vulnerable to wthdrawal n a bad state because t s unnsured and s protected only by the ablty to ext early and lqudate the underlyng collateral. To fx deas, t may be helpful to thnk of a smplfed two-step chan consstng of a hghlyleveraged ntermedary (HL) such as a broker-dealer along wth a money market fund (MMF). The HL buys the rsky asset, and ssues short-term repo aganst t, whch s then held by the MMF. MMF deposts and HL equty are owned by households. The MMF does not have captal or access to government depost nsurance, so for ts deposts to be rskless ts repo holdngs must also be rskless. Ths s the case because, f there s pessmstc news at tme 1, the MMF sezes the repo collateral and sells t at the fre-sale prce of k F. The maxmum amount of safe money that can be created by a shadow bank s therefore k F. Unlke tradtonal bank depostors protected by depost nsurance and bank equty captal, an MMF that nvests n repo cannot afford to sleep through tme 1; the MMF s ablty to pull the plug at ths nterm date s essental to keepng ts clam safe. 13

15 Unnsured shadow bankng deposts are therefore an endogenous form of hot money: they are unstable rather than stable short-term fundng. 8 The total value of clams the shadow bankng system can create usng the rsky asset as a backng s then gven by Value of MMF deposts Value of HL equty Money premum Expected cash flows V ( k) ( ) kf p( RkF) kf [ pr(1 p) kf]. S In any equlbrum where shadow banks hold asset, ther zero proft condton ensures that the S market value of asset must equal V ( k ). C. Equlbrum We assume that shadow banks face a downward-slopng demand curve at tme 1, so the fresale prce s a decreasng functon of the amount of the asset that s lqudated. Formally, let 0 be an exogenous parameter that ndexes the llqudty n the secondary market. We assume that (4) k(, )/ 0, so demand s downward slopng, and 2 k(, )/ 0, so more llqud assets have steeper demand curves. Fnally, as a normalzaton, we assume that k(,0) 1 for all : when 0the asset s perfectly lqud and there s never any fre-sale dscount. As shown n the Appendx, a fre-sale dscount of ths form can be mcro-founded as n Sten (2012). 9 Snce ntermedares are rsk-neutral and there are no benefts of dversfcaton bult nto our model, ntermedares wllngness to hold asset s not mpacted by ther holdngs of asset j. As a consequence, market equlbrum n any asset naturally decouples from that n asset j. An * equlbrum for asset s a such that 8 Households only derve monetary servces from clams that are guaranteed to be a safe store of value through tme 2. For unnsured shadow banks, safety requres early ext and hence a fre sale f the bad state occurs at tme 1. However, ex post, the expected value s hgher, albet rsker, f the assets are held to maturty. So what ensures that the assets wll be sold, thereby makng good on the promse of safety? For some shadow-bankng chans, there may be coordnaton problems that lead to runs and hence force fre sales. However, even n the absence of coordnaton problems e.g., f each MMF that nvests n repo s protected by a segregated pece of collateral commtment technologes can force the sale. For nstance, MMFs are prohbted from holdng the long-term assets that serve as collateral for repos, whch precommts them to a polcy of fre-sellng ths collateral. Whle ths commtment may lead to neffcences ex post, t s optmal for MMFs ex ante, as t helps to assure ther nvestors that ther clams wll be kept safe. 9 Specfcally, we assume that the rsky asset s sold to a thrd type of ntermedary (also owned by households) who has fxed resources and access to outsde nvestment opportuntes at t = 1. Snce these opportuntes are characterzed by dmnshng returns, shadow banks must offer larger dscounts to nduce these ntermedares to purchase more assets, thereby foregong ncreasngly productve outsde opportuntes. In ths context, dfferences across assets n reflect dfferences n the number of potental second-best holders of each asset.e., dfferences n asset specfcty. 14

16 V V k B S * * ( (, )) for (0,1) V V k B S * ( (0, )) 0 V V k B S * ( (1, )) 1. (5) The model admts both nteror outcomes and corner solutons, dependng on the asset-specfc values of z and φ. It s consstent wth the possblty that some assets (e.g., hghly llqud loans) are held only by banks, some (e.g., Treasures) are held predomnantly by shadow banks, and some (e.g., MBS) are held n sgnfcant amounts by both ntermedary types. S S Formally, snce V ( k(, ))/ ( V / k) ( k / ) 0, asset s held entrely by B S B S tradtonal banks when V V ( k(0, )) and entrely by shadow banks when V V ( k(1, )). 10 Snce shadow banks domnate tradtonal banks when there s no fre-sale dscount (.e., we always B S have V V (1) ), we only have a corner equlbrum where the assets s held entrely by tradtonal banks when k(0, ) 1. By contrast, f k(0, ) 1, then shadow banks must always hold some of the asset n equlbrum. At an nteror equlbrum where both tradtonal and shadow banks hold the asset, the fresale dscount k s such that both tradtonal and shadow banks earn zero profts by buyng the asset and ssung clams backed by t. Thus, at an nteror equlbrum, Margnal beneft of stable fundng: Margnal cost of stable fundng: avodng fre-sale lqudatons reduced money creaton * * p k F k F z (1 ) 1 (, ) (, ). Equaton (6) says that the mx between shadow banks and tradtonal banks must be such that margnal beneft of stable bank fundng equals the margnal cost of stable fundng. Stable fundng allows tradtonal banks to avod the fre-sale lqudaton dscount f there s pessmstc news at tme 1. Ths beneft of tradtonal banks relatve to shadow banks s captured by the left-hand-sde of (6). However, precsely because nvestors can get out early, the market can generate a larger amount of unstable short-term fundng than of stable fundng usng a gven asset as backng. Ths cost of tradtonal bankng relatve to shadow banks s captured by the rght-hand-sde of (6). In summary, although tradtonal banks have more stable fundng than shadow banks, ths stablty comes at a prce: tradtonal banks create fewer money-lke clams than shadow banks. Solvng equaton (6), the equlbrum fre-sale dscount s (6) 10 Implctly, by requrng 0,1, we are mposng a short-sale constrant for both tradtonal and shadow banks. 15

17 * * z (1 p) F k k(, ). F (1 p) F (7) Fnally, nvertng the k(, ) functon, the equlbrum fracton of asset held by shadow banks s 11 * 1 z (1 p) F k. F (1 p) F To take a smple parametrc example, assume k(, ) 1. In ths case, we have (8) 1 f * 0.e., the asset s held exclusvely by shadow banks f there s no fre-sale dscount and mn,1 mn,1, * * 1 k 1 ( F z) F (1 p) F (9) f 0, so that 0 as. * The equlbrum n our model s n the sprt of Mller (1977). Whle the aggregate mx of unstable ( ) versus stable fundng (1 ) for each asset s pnned down, so long as we are n an nteror equlbrum, any small ntermedary s ndfferent between settng up shop as a bank or as a shadow bank. Relatedly, the model s slent about the boundares of fnancal frms. In partcular, t s possble that a sngle nsttuton e.g., a unversal-style bank wth a broker-dealer afflate wnds up usng both the tradtonal and shadow bankng strateges. Equaton (6) says that the equlbrum fre-sale dscount s locally ndependent of asset llqudty at an nteror equlbrum where both tradtonal and shadow banks hold the asset. In ths regon, a change n asset llqudty mpacts the mx of asset holders an ncrease n llqudty rases the market share of banks but leaves the fre-sale dscount unchanged. However, f the assets are suffcently lqud ( s very low), the market share of tradtonal banks s eventually drven to zero, so the fre-sale dscount s ncreasng n asset llqudty for very low levels of. D. Comparatve statcs Ths smple model can be used to characterze the knds of assets for whch the tradtonal bankng model domnates. Two factors drve the tradeoff between tradtonal banks and shadow banks: the money premum for safe clams whch s controlled by and the strength of the fre-sale effect whch s controlled by. 11 Formally, the functon s mplctly defned by,. 16

18 Frst, f = 0 and k(, )/ 0, we have 0 the rsky asset s held entrely by * tradtonal banks. If there s no premum for safe clams, shadow bankng s domnated by tradtonal bankng: unstable short-term debt forces neffcent lqudatons and has no offsettng monetary benefts relatve to stable depost fundng. Conversely, f > 0 and = 0 so that k(,0) 1 for all, then 1 the asset s held entrely by shadow banks. The entre advantage of tradtonal banks stable fundng s that t enables them to rde out temporary departures of prce from fundamental value wthout lqudatng assets. If there s no fre-sale rsk and the prce at tme 1 always equals fundamental value, then stable fundng has no value; however, when > 0, rasng stable fundng s always more costly than rasng unstable fundng. The deal asset for a tradtonal bank s one that has very lttle fundamental cash-flow rsk (.e., z s hgh so rsk-based captal rules allow a bank to use t to back a lot of money-lke deposts), but that s exposed to meanngful nterm prce re-prcng rsk (.e., s hgh so fre-sale rsk looms large for ts shadow-bank counterparts). When both > 0 and > 0, there s a meanngful trade-off between the two ntermedaton structures and we wll have an nteror equlbrum. For an nteror equlbrum, we can ask how the equlbrum market shares of shadow banks ( ) and tradtonal banks ( * * 1 ) vary wth the exogenous model parameters. Dfferentatng equaton (8), we mmedately obtan the followng comparatve statcs for the fracton of an asset held by tradtonal banks: * : An ncrease n asset llqudty ncreases the equlbrum share held by * (1 ) / 0 tradtonal banks. By assumpton, an ncrease n asset llqudty makes the demand curve for fre-sale lqudatons at tme 1 steeper. Although a change n asset llqudty has no effect on the equlbrum level of the fre-sale dscount n (7), ths change alters the mappng between the ownershp mx and the fre-sale dscount n (8). When s hgh, the fre-sale dscount s hghly senstve to the volume of forced sales by shadow banks, so tradtonal banks end up holdng more of the asset n equlbrum. z : An ncrease n the worst-case cash flow z ncreases the share of the * (1 ) / 0 rsky asset held by tradtonal banks n equlbrum. An ncrease n z reduces the moneycreaton advantage of shadow banks relatve to tradtonal banks, and therefore needs to be 17

19 compensated by a rse n k * whch mples a rse n * 1 to restore equlbrum ndfference between tradtonal and shadow banks. We thnk of a hgher z as beng assocated wth less fundamental cash-flow rsk. Thus, all else equal, tradtonal banks have a comparatve advantage at holdng assets wth lttle fundamental cash-flow rsk. Taken together, these two results suggest that tradtonal banks have a comparatve advantage at holdng llqud fxed ncome assets.e., assets that may experence sgnfcant temporary prce dslocatons, but at the same tme, have only modest fundamental rsk. Agency MBS mght be a leadng example of such an asset, snce they are nsured aganst default rsk, but are consderably less lqud than Treasury securtes, and for a gven duraton, have more prce volatlty, snce there s sgnfcant varablty n the MBS-Treasury spread. The model also explans why banks are not well-suted to nvestng n equtes equtes smply have too much fundamental downsde rsk. Because ther value can fall very far over an extended perod of tme.e., because ther z s close to zero equtes cannot be effcently used as backng for safe two-perod clams. One reflecton of ths fact s that when banks do hold equtes, they face prohbtvely hgh regulatory captal requrements. 12 In contrast, to the extent that they are hghly lqud, equtes do make sutable collateral for very short-term repo fnancng and can be used to back some amount of shadow-bank money. What happens as the underlyng asset grows ncreasngly safe and lqud, tself becomng nearly money-lke? In practce, ths corresponds to askng who wll hold short-term Treasury blls. In ths lmtng case, both the benefts and the costs n equaton (6) vansh, so n our model the mx between tradtonal and shadow banks s ndetermnate. However, ths mx would be pnned down f we ntroduced a small overhead cost of tradtonal bankng that scaled wth assets under management, such as a cost of regulatory complance. In ths case, we would expect a non-bank vehcle such as a money market fund to hold the vast majorty of T-blls. In addton, we have the followng comparatve statcs whch mpact all assets: 3. : An ncrease n the money premum on safe clams lowers tradtonal * (1 ) / 0 banks equlbrum market share of all rsky assets. When the premum assocated wth 12 U.S. banks are currently requred to fnance any common stock holdngs wth at least 24% of loss-absorbng captal. The correspondng captal requrements for commercal loans and resdental mortgages are 8% and 4%, respectvely. 18

20 safe money-lke clams s hgher, the fre-sale dscount must rse to mantan equlbrum (.e., * k must fall), so the fracton of rsky assets held by shadow banks, *, must rse. 4. * (1 ) / p 0 : An ncrease n the probablty of good news at tme 1 lowers the share of all rsky assets held by tradtonal banks. When the nterm good state s more lkely, a larger fre-sale dscount (lower * k ) s needed to restore ndfference and the market share of shadow banks, *, must rse n equlbrum. Intutvely, bank s stable fundng structure functons as a costly form of nsurance aganst fre-sale rsk; ths nsurance naturally becomes less valuable when a fre sale s less lkely (.e., when p rses). Comparatve statc #3 suggests that an ncrease n the demand for safe, money-lke assets should trgger a mgraton of ntermedaton from tradtonal to shadow bankng. Indeed, some observers have argued that such an ncrease n money demand played a role n fuelng the rapd growth of shadow bankng pror to the recent fnancal crss. 13 Comparatve statc #4 suggests that ntermedaton actvty tends to mgrate away from tradtonal banks and towards shadow banks durng economc expansons when p s hgh. In ths way, our model provdes a way of understandng why tradtonal banks lost sgnfcant market share to shadow banks durng the runup to the recent fnancal crss. E. Model extensons We have delberately kept the model qute spare. Frst, we have assumed that the demand for safe clams s nfntely elastc and hence never satated (.e., households have lnear utlty over safe asset holdngs). In a more general model, the demand for safe clams would be downward-slopng (correspondng to concave utlty over safe clams), so the lqudty premum would declne wth the total quantty of safe clams provded by ntermedares. We can extend our model to allow the lqudty premum to be determned ths way n equlbrum. Holdng fxed the equlbrum money premum, our key results on the cross-secton of rsky assets stll obtan: tradtonal banks hold a larger share of more llqud assets and of assets wth less fundamental rsk. We have also mplctly assumed that, to the extent t s technologcally feasble, ntermedares use all rsky assets as fodder for backng money-lke clams. One mght extend the 13 See Bernanke (2005), Bernanke, Bertaut, Pounder DeMarco, and Kamn (2011), Gennaol et al (2013), Gournchas and Jeanne (2012), Krshnamurthy and Vssng-Jorgensen (2013), Caballero and Farh (2013), and Sunderam (2014). 19

21 model so that some rsky assets are not used to back money-lke clams and nstead are held drectly by households n equlbrum. For some rsky assets to not be used as fodder for backng safe clams, we would need to add an overhead cost of tradtonal bankng perhaps a cost that s ncreasng n tradtonal banks market share as n DeAngelo and Stulz (2014). Gong further, we could add assets lke Treasury blls that are perfectly safe even n the absence of any tranchng by fnancal ntermedares. As explored n Greenwood, Hanson, and Sten (2015) and Krshnamurthy and Vssng-Jorgensen (2015), wth downward-slopng demand for money-lke assets, changes n the supply of T-blls would depress the premum on safe clams, reducng the ncentve of shadow banks and tradtonal banks to bear the fre-sale and overhead costs ncurred n ntermedaton. F. Dscusson Whle banks asset holdngs are the most noteworthy complement to ther stable fundng structures, our model may help shed lght on other aspects of commercal banks modern busness model. Consder for example the brcks-and-mortar costs assocated wth bank depost-takng. We have estmated these costs to be qute hgh, averagng on the order of 1.30 percent of deposts over the perod from 1984 to These costs ultmately represent a choce banks could always choose to offer ther customers fewer and less attractve branch locatons, fewer opportuntes for nteractng wth a human teller, and so forth. One vew s that these amentes are smply a separable flow of servces to depostors, conceptually analogous to payng more nterest. However, an nterestng alternatve s that they represent a delberate effort to buld loyalty by creatng a form of swtchng costs. Investng n swtchng costs n ths way, and thereby further ncreasng depost stckness, would naturally be complementary to an overall busness model based on the premse of havng stable fundng. By contrast, a money market fund complex whch also takes deposts, but whch nvests exclusvely n short-term assets has less reason to care about depost stckness, and hence less ncentve to spend as heavly on a branch network. The model may also have somethng to say about the contrastng accountng practces of commercal banks and the nsttutons that play a crucal role n the shadow bankng system: money market funds, broker-dealers, and hedge funds. These market-based nsttutons typcally lack access to stable short-term fundng and operate on a mark-to-market accountng bass. Even f a declne n securty prces s temporary and drven by non-fundamental factors, t mpacts ther accountng earnngs. In contrast, accountng conventons for banks sheld ther earnngs from transtory changes n the unrealzed market value of loans or securtes. These temporary mparments flow through another lablty account called accumulated other comprehensve 20