Finance and Economics Discussion Series Divisions of Research & Statistics and Monetary Affairs Federal Reserve Board, Washington, D.C.

Size: px
Start display at page:

Download "Finance and Economics Discussion Series Divisions of Research & Statistics and Monetary Affairs Federal Reserve Board, Washington, D.C."

Transcription

1 Fnance and Economcs Dscusson Seres Dvsons of Research & Statstcs and Monetary Affars Federal Reserve Board, Washngton, D.C. Banks as Patent Fxed Income Investors Samuel G. Hanson, Andre Shlefer, Jeremy C. Sten, and Robert W. Vshny NOTE: Staff workng papers n the Fnance and Economcs Dscusson Seres (FEDS) are prelmnary materals crculated to stmulate dscusson and crtcal comment. The analyss and conclusons set forth are those of the authors and do not ndcate concurrence by other members of the research staff or the Board of Governors. References n publcatons to the Fnance and Economcs Dscusson Seres (other than acknowledgement) should be cleared wth the author(s) to protect the tentatve character of these papers.

2 Banks as Patent Fxed Income Investors * Samuel G. Hanson, Andre Shlefer, Jeremy C. Sten, and Robert W. Vshny Frst draft: February 2014 Abstract We examne the busness model of tradtonal commercal banks n the context of ther coexstence wth shadow banks. Whle both types of ntermedares create safe money-lke clams, they go about ths n very dfferent ways. Tradtonal banks create safe clams wth a combnaton of costly equty captal and fxed ncome assets that allows ther depostors to reman sleepy : they do not have to pay attenton to transent fluctuatons n the mark-to-market value of bank assets. In contrast, shadow banks create safe clams by gvng ther nvestors an early ext opton that allows them to seze collateral and lqudate t at the frst sgn of trouble. Thus tradtonal banks have a stable source of cheap fundng, whle shadow banks are subject to runs and fre-sale losses. These dfferent fundng models n turn nfluence the knds of assets that tradtonal banks and shadow banks hold n equlbrum: tradtonal banks have a comparatve advantage at holdng fxed-ncome assets that have only modest fundamental rsk, but are relatvely llqud and have substantal transtory prce volatlty. * The authors are from Harvard Unversty, Harvard Unversty, the Federal Reserve Board of Governors, and the Unversty of Chcago, respectvely. We would lke to thank semnar partcpants at Harvard for helpful comments as well as Malcolm Baker, John Campbell, Eduardo Dávla, Mhr Desa, Robn Greenwood, Davd Scharfsten, Ad Sunderam, and Paul Tucker for valuable suggestons. We thank Yueran Ma for excellent research assstance. The analyss and conclusons set forth here are those of the authors and do not ndcate concurrence by other members of the Board of Governors.

3 I. Introducton What s the busness of bankng? Do banks prmarly create value on the lablty sde of the balance sheet as n theores of bankng emphaszng lqudty creaton? Does the essence of bankng resde on the asset sde as n theores emphaszng banks ablty to montor borrowers? Or does the specal nature of banks derve from some synergy between ther assets and labltes? And what defnes the role played by tradtonal banks n a modern fnancal system where they compete wth market-based ntermedares such as shadow banks? To address these questons, we present a model n whch tradtonal and shadow banks coexst n the marketplace. We begn wth the premse that a prmary functon of both types of ntermedares s to create safe, money-lke clams that are of value to households because they are useful for transactons purposes. However, tradtonal banks and shadow banks go about ths task n dfferent ways. Tradtonal banks create safe clams wth a combnaton of costly equty captal and asset holdngs that have relatvely safe long-run payoffs. Ths structure allows ther depostors to reman sleepy : they do not have to pay attenton to transent fluctuatons n the mark-to-market value of bank assets. In contrast, when shadow banks such as broker-dealers and hedge funds create money-lke clams such as repurchase agreements, they use less of the costly equty captal, but hold assets that can be sezed and easly lqudated at the frst sgn of trouble by nvestors who must reman vglant. A central feature of our model s that such lqudatons by shadow banks create fre-sale effects, n that they temporarly push asset prces below fundamental value. So, on the one hand, tradtonal banks more stable depost fundng structure has an advantage, n that t gves them the ablty to hold nvestments to maturty, rdng out transtory valuaton shocks untl prces revert to fundamental values. On the other hand, ths stablty comes at a cost, as t requres tradtonal banks to put up more captal aganst a gven nvestment than shadow banks. Because the endogenous fresale dscount s greater when shadow banks hold more of an asset, ths tradeoff pns down the equlbrum holdngs of any gven asset category across ntermedary types. In partcular, n an nteror equlbrum, 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 that a tradtonal bank pays to obtan more stable fundng. Alternatvely, for some types of assets we can have corner solutons, n whch case the model speaks to the specalzaton of tradtonal and shadow banks n asset holdngs. 1

4 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 wth nvestng n fxed-ncome assets that have only modest fundamental rsk, but that 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 busness of commercal bankng, and s what fundamentally dstngushes tradtonal banks from shadow banks: tradtonal banks are patent nvestors that can nvest n llqud fxed-ncome 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). 1 We see transtory non-fundamental movements n asset prces as 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. After developng the model, we use the Fnancal Accounts of the Unted States (formerly the Flow of Funds) to provde some smple aggregate evdence consstent wth the model s key predctons. Specfcally, lookng across fxed ncome asset classes, 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. There s a vast lterature on the economc role of banks. Our work connects most closely to two strands of ths lterature. One strand, formalzed frst by Gorton and Pennacch (1990), focuses on the depost-takng functon of banks, and stresses ther role n the creaton of labltes whch, precsely because of ther safety and mmunty from adverse-selecton problems, are useful as a transactons medum. Banks are specal n ths vew because they are the nsttutons that create prvate, or nsde, money. 2 1 Alternatvely, the mechansm could be lqudaton costs that stem from asset specfcty or adverse selecton. 2 Recent papers n ths ven nclude Dang, Gorton and Holmstrom (2013), DeAngelo and Stulz (2013), Gennaol et al (2013), Gorton and Ordonez (2014), Sten (2012), and Krshnamurthy and Vssng-Jorgensen (2013). 2

5 Ths lablty-centrc vew of banks surely captures an mportant element of realty. In partcular, t 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 banks are almost always heavly depost-fnanced. At the same tme, ths lablty-centrc vew alone cannot be a complete theory of bankng, because t does not speak to the asset sde of bank balance sheets. 3 For example, although t does not necessarly follow as a logcal matter, the lablty-centrc vew has led some observers to advocate narrow bankng proposals, whereby bank-created money s backed entrely by safe lqud assets, such as Treasury blls. 4 And yet as a postve descrpton of commercal bankng, narrow bankng s very far from what we observe n the world. Indeed, we show that money creaton through depost-takng s too expensve for narrow bankng to be a vable busness strategy for commercal banks. 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 nature of 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. Damond and Dybvg emphasze depost nsurance as the source of stablty that keeps depostors sleepy and prevents runs. We recognze that depost nsurance s crtcal n realty, and n fact could play a key role n a verson of our model extended to consder the tal rsk of assets. But here we analyze an addtonal reason for the stablty of bank labltes not present n Damond and Dybvg, namely banks selecton of the assets n ther portfolos. 5 Specfcally, we emphasze that precsely as a mechansm of ensurng the stablty of ther labltes banks specalze n holdng fxed ncome assets that may be subject to nterm prce volatlty, but have relatvely predctable long run cash flows. In other words, n addton to 3 A smlar observaton can be made about asset-centrc theores that focus solely on banks role as delegated montors (Damond (1984)). Here banks are seen as a mechansm for dealng wth the nformaton and ncentve problems that would otherwse make t dffcult for credt to be extended to opaque borrowers. Because ths work s slent on the structure of bank labltes, t does not draw a dstncton between banks and other non-bank lenders. 4 See Pennacch (2012) for a detaled dscusson of narrow bankng proposals. 5 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. Gennaol, Shlefer, and Vshny (2013) argue that a central functon of banks s to provde safe clams, but emphasze asset-sde dversfcaton and tranchng as technologes for backng such safe labltes. 3

6 government depost nsurance, conservatve asset choces play a crucal role n supportng stable money creaton. In ths regard, we note that commercal banks hold not only loans, but also marketable securtes, often n very substantal amounts. Moreover, these securtes holdngs have a partcular pattern. Banks tend to stay away from the most lqud securtes, such as Treasures, and concentrate ther holdngs n securtes that are less lqud and whose market prces are more volatle. These nclude mortgage-backed securtes, asset-backed securtes, and corporate bonds. At the same tme, banks do not hold equtes, whose cash flows are too rsky. These patterns provde an mportant clue as to the busness of tradtonal bankng more generally, and to the complementarty between asset and lablty structures, whch our model seeks to explan. 6 Our work s also related to several other famlar themes. Frst, a number of papers have explored the jont roles of banks and securtes markets n allocatng credt and satsfyng the demand for lqudty (Holmstrom and Trole 1997, 2011; Damond 1997). Second, a recent body of work has studed the shadow bankng system and ts role n the fnancal crss (Brunnermeer and Pedersen 2009; Coval, Jurek, and Stafford 2009a and 2009b; Shlefer and Vshny 2010; Gorton and Metrck 2010 and 2011; Shn 2009; Sten 2012; Gennaol et al 2013; Kacperzcyk and Schnabl 2013; Krshnamurthy, Nagel, and Orlov 2013; Chernenko and Sunderam 2013; Sunderam 2013; Weymuller 2013, Morera and Savov 2014). Fnally, the evdence we develop usng the Fnancal Accounts draws on research whch seeks to measure the msmatch between the lqudty of ntermedary assets and labltes (Brunnermeer, Gorton, and Krshnamurthy 2011 and 2013 and Ba, Krshnamurthy, and Weymuller 2013). The plan for the paper s as follows. In the next secton, we present some motvatng evdence on the nature of the assets and labltes of tradtonal banks, wth partcular emphass on banks securtes holdngs. In Secton III, we present our model, n whch tradtonal banks and shadow banks compete as potental buyers of assets wth varyng degrees of fundamental and lqudty rsk. The model yelds predctons that we then examne emprcally n Secton IV. Secton V dscusses some addtonal features of modern bankng that appear to be consstent wth the model. Secton VI brefly dscusses polcy mplcatons of the model and Secton VII concludes. 6 Taken lterally, the Damond-Dybvg (1983) model does not admt a ratonale for banks to hold marketable securtes; see Jackln (1987). And even f taken less lterally, t does not make any predctons about the knds of securtes that banks are expected to hold. 4

7 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 the rato was almost sx tmes hgher, at 40.7%. 7 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 7 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 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., 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 6

9 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. 8 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%). 9 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. 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 8 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%. 9 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

10 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 a collecton of assets wth dfferent degrees of fundamental and lqudty rsk. The essence of the tradeoff s that banks pay more by rasng more equty captal to create money-lke clams that are not only safe for nvestors n the short-run, but also stable, and unlkely to run when there s bad news. Ths stablty allows banks to avod neffcent fre sales of ther assets. 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 8

11 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 and Stulz (2013), 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. 9

12 Tme t = 0 Intermedares purchase the rsky asset and ssue safe and rsky clams to households Tme t = 1 Bad state 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 R 1-p q R Fundamental value after bad news at t=1 s F = qr + (1-q)z. However, the market prce s only k F F. 1-q z The tmng of the model s as follows. Each 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. At tme 1, there s an nterm news event about the future economc state. Wth probablty p, the nterm news s good, 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 bad, whch means that there s a subsequent probablty of (1 q) of the bad state and low payoff on all assets at tme 2. Thus, n the bad-news state at tme 1, the fundamental value of asset s F = qr + (1-q)z. 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 bad 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. B. Intermedaton structures To examne the dfferent ways the rsky assets can be held and used as backng to create safe clams, we consder two ntermedaton structures: tradtonal bankng and shadow bankng. At t = 0, households can nvest n ether tradtonal bank deposts 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 10

13 n expectaton at t = 2. In equlbrum, 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 tradtonal and shadow banks vary as we change the propertes of the asset n queston. B.1. Tradtonal banks A tradtonal bank uses a stable, hold-to-maturty strategy for generatng absolutely safe short-term clams. The bank plans to always hold the rsky asset to maturty, so the maxmum amount of safe money-lke clams that can be created s z, whch s the worst-case payoff at tme 2. The remander of the asset purchase must be fnanced by rasng rsky equty captal whch s more expensve. Snce asset always pays off at least z, a depostor n a tradtonal bank can sleep through whatever news comes at tme 1 and stll be assured of havng a safe clam. In other words, a bank has enough captal so that ts deposts are endogenously stcky; there s no reason for bank depostors ever to wthdraw at date 1, so the bank never has to sell assets at a fre-sale dscount. Alternatvely, one can thnk of the bank as havng acqured government-backed depost nsurance whch allows depostors to sleep through tme 1 and the depost nsurer as havng mposed a captal requrement on the bank that s suffcent to reduce ts expected losses to zero. The total value of clams the bank can ssue at tme 0 usng the rsky asset as backng s Value of bank deposts Value of bank equty B V ( ) z ( p(1 p) q)( Rz ) Money premum Expected cash flows z [ pr(1 p) F], (3) where, agan, F = qr + (1 q)z s the fundamental value of asset n the bad state at t = 1. In any equlbrum where banks hold securty, banks zero proft condton ensures that the market value of securty 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 they can use the rsky asset to back z unts of safe money-lke clams. B.2. Shadow banks An alternatve ntermedaton structure s a shadow bank, whch s a composte structure consstng of a hghly-leveraged ntermedary (HL) such as a broker-dealer or a hedge fund, along 11

14 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 has no captal, so for ts deposts to be rskless nvestments for households the repo that the MMF holds must also be made rskless. The way these repo clams are kept safe s that f there s bad news at tme 1, the MMF sezes the 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 the tradtonal bank depostors protected by 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. Shadow bankng deposts are thus an endogenous form of hot money: they are unstable rather than stable short-term fundng. 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 S V ( k) ( ) kf p( RkF) Money premum Expected cash flows kf [ pr(1 p) kf]. (4) In any equlbrum where shadow banks hold securty, ther zero proft condton ensures that the S market value of securty 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 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) Specfcally, we assume that the rsky asset s sold to a thrd type of ntermedary (also owned by households) who have fxed resources and access to outsde nvestment opportuntes at t = 1. Snce these opportuntes are characterzed by dmnshng returns to scale, shadow banks must offer larger dscounts relatve to fundamental value to nduce these ntermedares to purchase more assets, thereby foregong ncreasngly productve outsde opportuntes. In ths context, 12

15 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 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 ether nteror outcomes or 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, securty 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, )). 11 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 securty, the fre-sale 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, we have Margnal beneft of stable fundng: Margnal cost of stable fundng: avodng fre-sale lqudatons reduced money creaton * * (1 p) 1 k(, ) F k(, ) F z. Equaton (6) s the central equaton of the model. It says that the mx between shadow banks and tradtonal banks must be such that margnal beneft of stable bank fundng equals the margnal cost (6) dfferences across assets n reflect dfferences n the number of potental second-best holders of each asset.e., dfferences n asset specfcty. 11 Implctly, by requrng 0,1, we are mposng a short-sale constrant for both tradtonal and shadow banks. 13

16 of stable fundng. 12 Stable fundng allows tradtonal banks to avod the fre-sale lqudaton dscount f the bad state occurs 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 * * 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 13 * 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 f 0, so that mn,1 mn,1, * * 1 k 1 ( F z) F (1 p) F 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 e.g., whether a holdng company wnds up housng both tradtonal and shadow bankng operatons. 12 The left-hand sde of equaton (6) s the prvate beneft of avodng fre-sales that s nternalzed by an ndvdual ntermedary choosng between the tradtonal and shadow bankng forms. As Sten (2012) shows, ths dffers from the total socal benefts of avodng fre-sales because bndng, prce-dependent collateral constrants open the door to pecunary externaltes. We return to ths pont n Secton VI where we explore the polcy mplcatons of the model. 13 Formally, the functon s mplctly defned by,. 14

17 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 The model can be used to characterze the knds of assets for whch the tradtonal bankng model domnates. To do so, we must examne the roles of the two factors that 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. 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 a bank can 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). In general, when both > 0 and > 0, there s a meanngful trade-off between the two ntermedaton structures and we wll have an nteror equlbrum. In the case of an nteror equlbrum, we can ask how the equlbrum market shares of shadow banks ( ) and tradtonal banks ( * * 1 ) vary wth the exogenous model parameters. 15

18 Specfcally, dfferentatng equaton (8), we mmedately obtan the followng comparatve statcs for the fracton of an asset held by tradtonal banks: 1. : 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. 2. : An ncrease n the worst-case cash flow z ncreases the share of the * (1 ) / z 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 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 can 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 even absent any nsttutonal or regulatory constrants, banks would endogenously choose to avod 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 to create safe two-perod clams. As such, they are not good collateral for bank money. By contrast, to the extent that they are hghly lqud, they do make sutable collateral for very short-term repo fnancng. In other words, equtes can be used to back some amount of shadow-bank money. 16

19 In addton, we have the followng comparatve statcs whch mpact all assets: : 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 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. * (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. 14 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 summary, 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. IV. Further Evdence In ths secton, we provde some smple aggregate evdence bearng on the model s predctons. We thnk of ths analyss more as a synthess of known hgh-level facts about the structure of fnancal ntermedaton than as a true test of the model. We frst descrbe how we take the model to the data, then our measurement approach, and fnally the results of some smple crosssectonal regressons suggested by the model. 14 See for nstance Bernanke (2005), Gennaol et al (2013), Gournchas and Jeanne (2012), Krshnamurthy and Vssng- Jorgensen (2013), and Caballero and Farh (2013). 17

20 A. Takng the model to the data A.1. The cross-secton of asset classes A key testable mplcaton of our model s that, all else equal, tradtonal banks should hold a hgher market share n more llqud assets:. * (1 ) / 0 Predcton 1: Lookng across assets and holdng constant fundamental asset rsk, banks should have a larger market share n asset classes that are more llqud. Our model features just two ntermedary types: tradtonal banks wth stable fundng and shadow banks wth unstable fundng. In realty, there are many ntermedary types wth a range of fundng stablty. Generalzng our theory, we would expect ntermedares wth more stable fundng to hold more llqud assets wth hgh fre-sale rsk. Predcton 2: Lookng across assets and holdng constant fundamental asset rsk, more llqud asset classes should be held by ntermedary types wth greater fundng stablty. A.2. The cross-secton of ntermedary types Snce our theory has predctons for the cross-secton of asset types, t naturally generates related predctons for the cross-secton of ntermedary types. Specfcally, the portfolo share of shadow banks n asset s w Q * S* N * k 1 k Q k, (9) and the portfolo share of tradtonal banks n asset s w * B* (1 ) Q N * k 1 k (1 ) Q k. It follows trvally from the comparatve statcs derved above that w S* / 0, (10) w S* / z 0, w B* / 0, and w B* / z 0. In other words, shadow bank portfolos are tlted towards assets that are more lqud or have more fundamental downsde-rsk, whereas tradtonal bank portfolos are tlted towards assets that are more llqud and have less fundamental downsde-rsk. The average llqudty of assets held by shadow banks s S* N S* 1 w, (11) and the average llqudty of asset held by commercal banks s B* N B* 1 w. (12) 18

can basic entrepreneurship transform the economic lives of the poor?

can basic entrepreneurship transform the economic lives of the poor? can basc entrepreneurshp transform the economc lves of the poor? Orana Bandera, Robn Burgess, Narayan Das, Selm Gulesc, Imran Rasul, Munsh Sulaman Aprl 2013 Abstract The world s poorest people lack captal

More information

The Relationship between Exchange Rates and Stock Prices: Studied in a Multivariate Model Desislava Dimitrova, The College of Wooster

The Relationship between Exchange Rates and Stock Prices: Studied in a Multivariate Model Desislava Dimitrova, The College of Wooster Issues n Poltcal Economy, Vol. 4, August 005 The Relatonshp between Exchange Rates and Stock Prces: Studed n a Multvarate Model Desslava Dmtrova, The College of Wooster In the perod November 00 to February

More information

Do Firms Maximize? Evidence from Professional Football

Do Firms Maximize? Evidence from Professional Football Do Frms Maxmze? Evdence from Professonal Football Davd Romer Unversty of Calforna, Berkeley and Natonal Bureau of Economc Research Ths paper examnes a sngle, narrow decson the choce on fourth down n the

More information

DISCUSSION PAPER. Should Urban Transit Subsidies Be Reduced? Ian W.H. Parry and Kenneth A. Small

DISCUSSION PAPER. Should Urban Transit Subsidies Be Reduced? Ian W.H. Parry and Kenneth A. Small DISCUSSION PAPER JULY 2007 RFF DP 07-38 Should Urban Transt Subsdes Be Reduced? Ian W.H. Parry and Kenneth A. Small 1616 P St. NW Washngton, DC 20036 202-328-5000 www.rff.org Should Urban Transt Subsdes

More information

Why Don t We See Poverty Convergence?

Why Don t We See Poverty Convergence? Why Don t We See Poverty Convergence? Martn Ravallon 1 Development Research Group, World Bank 1818 H Street NW, Washngton DC, 20433, USA Abstract: We see sgns of convergence n average lvng standards amongst

More information

The Global Macroeconomic Costs of Raising Bank Capital Adequacy Requirements

The Global Macroeconomic Costs of Raising Bank Capital Adequacy Requirements W/1/44 The Global Macroeconomc Costs of Rasng Bank Captal Adequacy Requrements Scott Roger and Francs Vtek 01 Internatonal Monetary Fund W/1/44 IMF Workng aper IMF Offces n Europe Monetary and Captal Markets

More information

DISCUSSION PAPER. Is There a Rationale for Output-Based Rebating of Environmental Levies? Alain L. Bernard, Carolyn Fischer, and Alan Fox

DISCUSSION PAPER. Is There a Rationale for Output-Based Rebating of Environmental Levies? Alain L. Bernard, Carolyn Fischer, and Alan Fox DISCUSSION PAPER October 00; revsed October 006 RFF DP 0-3 REV Is There a Ratonale for Output-Based Rebatng of Envronmental Leves? Alan L. Bernard, Carolyn Fscher, and Alan Fox 66 P St. NW Washngton, DC

More information

The Developing World Is Poorer Than We Thought, But No Less Successful in the Fight against Poverty

The Developing World Is Poorer Than We Thought, But No Less Successful in the Fight against Poverty Publc Dsclosure Authorzed Pol c y Re s e a rc h Wo r k n g Pa p e r 4703 WPS4703 Publc Dsclosure Authorzed Publc Dsclosure Authorzed The Developng World Is Poorer Than We Thought, But No Less Successful

More information

Income per natural: Measuring development as if people mattered more than places

Income per natural: Measuring development as if people mattered more than places Income per natural: Measurng development as f people mattered more than places Mchael A. Clemens Center for Global Development Lant Prtchett Kennedy School of Government Harvard Unversty, and Center for

More information

Should marginal abatement costs differ across sectors? The effect of low-carbon capital accumulation

Should marginal abatement costs differ across sectors? The effect of low-carbon capital accumulation Should margnal abatement costs dffer across sectors? The effect of low-carbon captal accumulaton Adren Vogt-Schlb 1,, Guy Meuner 2, Stéphane Hallegatte 3 1 CIRED, Nogent-sur-Marne, France. 2 INRA UR133

More information

WHICH SECTORS MAKE THE POOR COUNTRIES SO UNPRODUCTIVE?

WHICH SECTORS MAKE THE POOR COUNTRIES SO UNPRODUCTIVE? MŰHELYTANULMÁNYOK DISCUSSION PAPERS MT DP. 2005/19 WHICH SECTORS MAKE THE POOR COUNTRIES SO UNPRODUCTIVE? BERTHOLD HERRENDORF ÁKOS VALENTINYI Magyar Tudományos Akadéma Közgazdaságtudomány Intézet Budapest

More information

Assessing health efficiency across countries with a two-step and bootstrap analysis *

Assessing health efficiency across countries with a two-step and bootstrap analysis * Assessng health effcency across countres wth a two-step and bootstrap analyss * Antóno Afonso # $ and Mguel St. Aubyn # February 2007 Abstract We estmate a sem-parametrc model of health producton process

More information

Boosting as a Regularized Path to a Maximum Margin Classifier

Boosting as a Regularized Path to a Maximum Margin Classifier Journal of Machne Learnng Research 5 (2004) 941 973 Submtted 5/03; Revsed 10/03; Publshed 8/04 Boostng as a Regularzed Path to a Maxmum Margn Classfer Saharon Rosset Data Analytcs Research Group IBM T.J.

More information

Complete Fairness in Secure Two-Party Computation

Complete Fairness in Secure Two-Party Computation Complete Farness n Secure Two-Party Computaton S. Dov Gordon Carmt Hazay Jonathan Katz Yehuda Lndell Abstract In the settng of secure two-party computaton, two mutually dstrustng partes wsh to compute

More information

What to Maximize if You Must

What to Maximize if You Must What to Maxmze f You Must Avad Hefetz Chrs Shannon Yoss Spegel Ths verson: July 2004 Abstract The assumpton that decson makers choose actons to maxmze ther preferences s a central tenet n economcs. Ths

More information

Ciphers with Arbitrary Finite Domains

Ciphers with Arbitrary Finite Domains Cphers wth Arbtrary Fnte Domans John Black 1 and Phllp Rogaway 2 1 Dept. of Computer Scence, Unversty of Nevada, Reno NV 89557, USA, jrb@cs.unr.edu, WWW home page: http://www.cs.unr.edu/~jrb 2 Dept. of

More information

4.3.3 Some Studies in Machine Learning Using the Game of Checkers

4.3.3 Some Studies in Machine Learning Using the Game of Checkers 4.3.3 Some Studes n Machne Learnng Usng the Game of Checkers 535 Some Studes n Machne Learnng Usng the Game of Checkers Arthur L. Samuel Abstract: Two machne-learnng procedures have been nvestgated n some

More information

From Computing with Numbers to Computing with Words From Manipulation of Measurements to Manipulation of Perceptions

From Computing with Numbers to Computing with Words From Manipulation of Measurements to Manipulation of Perceptions IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS I: FUNDAMENTAL THEORY AND APPLICATIONS, VOL. 45, NO. 1, JANUARY 1999 105 From Computng wth Numbers to Computng wth Words From Manpulaton of Measurements to Manpulaton

More information

EVERY GOOD REGULATOR OF A SYSTEM MUST BE A MODEL OF THAT SYSTEM 1

EVERY GOOD REGULATOR OF A SYSTEM MUST BE A MODEL OF THAT SYSTEM 1 Int. J. Systems Sc., 1970, vol. 1, No. 2, 89-97 EVERY GOOD REGULATOR OF A SYSTEM MUST BE A MODEL OF THAT SYSTEM 1 Roger C. Conant Department of Informaton Engneerng, Unversty of Illnos, Box 4348, Chcago,

More information

Who are you with and Where are you going?

Who are you with and Where are you going? Who are you wth and Where are you gong? Kota Yamaguch Alexander C. Berg Lus E. Ortz Tamara L. Berg Stony Brook Unversty Stony Brook Unversty, NY 11794, USA {kyamagu, aberg, leortz, tlberg}@cs.stonybrook.edu

More information

UPGRADE YOUR PHYSICS

UPGRADE YOUR PHYSICS Correctons March 7 UPGRADE YOUR PHYSICS NOTES FOR BRITISH SIXTH FORM STUDENTS WHO ARE PREPARING FOR THE INTERNATIONAL PHYSICS OLYMPIAD, OR WISH TO TAKE THEIR KNOWLEDGE OF PHYSICS BEYOND THE A-LEVEL SYLLABI.

More information

TrueSkill Through Time: Revisiting the History of Chess

TrueSkill Through Time: Revisiting the History of Chess TrueSkll Through Tme: Revstng the Hstory of Chess Perre Dangauther INRIA Rhone Alpes Grenoble, France perre.dangauther@mag.fr Ralf Herbrch Mcrosoft Research Ltd. Cambrdge, UK rherb@mcrosoft.com Tom Mnka

More information

Turbulence Models and Their Application to Complex Flows R. H. Nichols University of Alabama at Birmingham

Turbulence Models and Their Application to Complex Flows R. H. Nichols University of Alabama at Birmingham Turbulence Models and Ther Applcaton to Complex Flows R. H. Nchols Unversty of Alabama at Brmngham Revson 4.01 CONTENTS Page 1.0 Introducton 1.1 An Introducton to Turbulent Flow 1-1 1. Transton to Turbulent

More information

(Almost) No Label No Cry

(Almost) No Label No Cry (Almost) No Label No Cry Gorgo Patrn,, Rchard Nock,, Paul Rvera,, Tbero Caetano,3,4 Australan Natonal Unversty, NICTA, Unversty of New South Wales 3, Ambata 4 Sydney, NSW, Australa {namesurname}@anueduau

More information

MANY of the problems that arise in early vision can be

MANY of the problems that arise in early vision can be IEEE TRANSACTIONS ON PATTERN ANALYSIS AND MACHINE INTELLIGENCE, VOL. 26, NO. 2, FEBRUARY 2004 147 What Energy Functons Can Be Mnmzed va Graph Cuts? Vladmr Kolmogorov, Member, IEEE, and Ramn Zabh, Member,

More information

Alpha if Deleted and Loss in Criterion Validity 1. Appeared in British Journal of Mathematical and Statistical Psychology, 2008, 61, 275-285

Alpha if Deleted and Loss in Criterion Validity 1. Appeared in British Journal of Mathematical and Statistical Psychology, 2008, 61, 275-285 Alpha f Deleted and Loss n Crteron Valdty Appeared n Brtsh Journal of Mathematcal and Statstcal Psychology, 2008, 6, 275-285 Alpha f Item Deleted: A Note on Crteron Valdty Loss n Scale Revson f Maxmsng

More information

The CBOE Volatility Index - VIX

The CBOE Volatility Index - VIX Whte Paper he CBOE Volatlty Index - VIX he powerful and flexble tradng and rsk managment tool from the Chcago Board Optons Exchange HE CBOE VOLAILIY INDEX - VIX In 993, the Chcago Board Optons Exchange

More information

Ensembling Neural Networks: Many Could Be Better Than All

Ensembling Neural Networks: Many Could Be Better Than All Artfcal Intellgence, 22, vol.37, no.-2, pp.239-263. @Elsever Ensemblng eural etworks: Many Could Be Better Than All Zh-Hua Zhou*, Janxn Wu, We Tang atonal Laboratory for ovel Software Technology, anng

More information

As-Rigid-As-Possible Image Registration for Hand-drawn Cartoon Animations

As-Rigid-As-Possible Image Registration for Hand-drawn Cartoon Animations As-Rgd-As-Possble Image Regstraton for Hand-drawn Cartoon Anmatons Danel Sýkora Trnty College Dubln John Dnglana Trnty College Dubln Steven Collns Trnty College Dubln source target our approach [Papenberg

More information

Clean Development Mechanism and Development of a Methodology for the Recycling of Municipal Solid Waste

Clean Development Mechanism and Development of a Methodology for the Recycling of Municipal Solid Waste Clean Development Mechansm and Development of a Methodolog for the Recclng of Muncpal Sold Waste CONTACT Charles Peterson, World Bank Jule Godn, World Bank Contact name: Charles Peterson Jule Godn Organzaton:

More information