Financial Innovations, Idiosyncratic Risk, and the Joint Evolution of Real and Financial Volatilities

Transcription

1 Fnancal Innovatons, Idosyncratc Rsk, and the Jont Evoluton of Real and Fnancal Volatltes J. Chrstna Wang * Research Department Federal Reserve Bank of Boston November 2006 Abstract: Ths paper presents a model n whch fnancal nnovatons explan three wdely dscussed stylzed facts regardng trends n economc volatlty over the past two decades. Aggregate volatlty of real varables such as output has fallen. In partcular, the covarance between frm and ndustry actvtes has declned, and so has employment volatlty for the majorty of frms. In contrast, the volatlty of quanttes of fnancal varables has ncreased at both the frm and aggregate level. The model lnks these outcomes to a sngle hypotheszed cause: advances n fnancal technology brought about by a declnng cost of nformaton processng. As a result, the margnal cost of external funds has lkely declned, reducng the need for frms to smooth cash flows. Frms, tradng off cash-flow vs. producton smoothng, therefore have more ncentve to smooth producton. Ths explans why fnancal volatlty may go up as real volatlty goes down. Moreover, fnancal nnovatons have lkely also altered the composton of volatlty toward a greater share of dosyncratc rsk, by facltatng dversfcaton and thus lowerng the premum demanded on dosyncratc rsk. At the margn, the cost advantage to projects wth dosyncratc returns reduces the covarance of fnancal as well as real actvtes across frms. Snce varance and covarance of real quanttes trend n the same drecton, real aggregate volatlty declnes. But the net effect on fnancal varables s ambguous and so can yeld greater aggregate volatlty. The paper then presents evdence that the share of dosyncratc rsk has rsen n bank portfolos, ndcatng that the same has occurred for ndvdual borrowers as well. I am grateful to Susanto Basu and John Fernald for much generous support, and to Daron Acemoglu, Julo Rotemberg and Scott Schuh for helpful dscussons. Many thanks also to Adrenne Hathaway, and especally to Nc Duquette for ther able research assstance. All errors reman the sole responsblty of the author, and the vews expressed here do not necessarly represent those of the Federal Reserve System. * E-mal: chrstna.wang@bos.frb.org

2 Introducton It s by now a well-known fact that U.S. economc actvty n the aggregate has become less volatle snce the md-980s. The behavor of fnancal varables, on the other hand, roughly tracks the output varance of publcly-traded frms, whch appears to have rsen over the past four decades. However, strkng new evdence based on employment data shows that prvate frms have become less volatle durng the same perod over whch publc frms have become more volatle. Aggregate employment volatlty, domnated by the behavor of the prvate frms, therefore has declned. Fnally, several studes have shown that there has been a reducton n the covarance of output growth among ndustres and frms; ths also helps fll the apparent nconsstency between rsng output volatlty n large frms and declnng volatlty n the aggregate. Ths paper develops a model that can smultaneously explan ths collage of fndngs, n partcular ) why the volatlty of real varables (such as output and employment) may decrease even whle the volatlty of fnancal varables (such as dvdends and net borrowng) ncreases, and 2) why dosyncratc rsk has grown n mportance and led to fallng cross-secton covarance n both real and fnancal varables. The paper shows that these seemngly dsparate trends can plausbly be the jont outcomes of a common cause technologcal progress n the fnancal sector. The paper posts that advances n nformaton and communcaton technology (ICT) have greatly lowered the margnal cost of collectng, processng and transmttng nformaton n general, and credt nformaton n partcular (for example, by usng computer-based credt scorng models). As a result, banks today make loans to more borrowers, and also to smaller borrowers. If banks face a convex cost of external funds, due to asymmetrc nformaton problems or a convex cost of supplyng depost servces, then t s optmal for them to smooth the total volatlty of ther cash flows. When banks loan portfolos were far from well dversfed for varous reasons, what Apart from geographc concentraton of loans due to regulatory constrants, other reasons nclude the desre to utlze ncreasng returns to scale assocated wth accumulated specal knowledge of a partcular ndustry or regon.

3 affected a portfolo s total return varablty at the margn was each addtonal loan s total volatlty, not just ts systematc volatlty. Thus, the expected yeld requred by lenders tradtonally rose not only wth a loan s systematc rsk but also wth ts dosyncratc rsk. 2 Snce cheaper and better ICT lowers the cost of makng each extra loan, standard ntuton says that a smaller number of banks wll hold larger numbers of loans n each of ther portfolos. Each loan s dosyncratc rsk would thus account for a fallng share of ts margnal contrbuton to the portfolo s total volatlty, whch would eventually come to be domnated by the loans covarances wth the systematc factors. As a result, the requred rate of return on each loan would come to depend ncreasngly on the loan s systematc rsk. In the lmt, any ncrease n return varablty due to loan-specfc volatlty would not rase the nterest rate a borrower expects to pay ex ante. The dversfcaton-enhancng effect from an ncreasng number of loans n each portfolo, however, can be more than offset by shfts n equlbrum credt supply toward borrowers whose returns are less correlated wth the systematc factors. So the degree of dversfcaton n bank loan portfolos may n fact even fall over tme. Ths seemngly counterntutve outcome can arse because the same force a relatvely lower rsk premum on dosyncratc rsk acts on banks as well as ther borrowers. Frst, for the borrowng frms, a fallng premum on dosyncratc rsk relatve to that on systematc rsk a relatve prce change wll confer a cost advantage to frms wth returns less correlated wth the systematc factors. Furthermore, facng the lower relatve prce on dosyncratc rsk, borrowers may fnd t optmal to adopt operaton plans that lead to less exposure to systematc rsk. Consequently, such projects wll account for a bgger share of the potental demand for credt at each bank. Such a demand shft, however, may or may not offset the postve effect on portfolo dversfcaton from havng a larger number of loans. Net change n the dversfcaton of a loan pool as a whole wll ultmately be determned by the bank s choce, both as a lender to nonfnancal frms and as a 2 By comparson, the promsed yeld nterest rate charged n a loan contract ex ante should rse n a borrower s total rsk, ncludng her dosyncratc rsk, even n a perfectly dversfed portfolo because hgher dosyncratc volatlty too rases the probablty of default. 2

4 borrower n fnancal markets. Dversfcaton at the portfolo level wll on net declne unambguously f banks also face a lower relatve cost of dosyncratc rsk when borrowng n the markets, snce each bank should react lke ts borrowers and rase the overall exposure to bank-specfc rsk. The rsk premum on bank-specfc volatlty falls because the fnancal markets have also become more effcent at processng credt nformaton owng to ICT and the ensung nnovatons. Ths paper s emprcal secton then nvestgates whether, as would be predcted by the above reasonng, the degree of dversfcaton has n fact decreased over tme for loan portfolos of a gven sze. And, usng stock return data of publcly traded bank holdng companes, t does ndeed fnd evdence that dversfcaton has not ncreased n these ntermedares. Ths suggests that these bank holdng companes have altered the composton of ther loan pools so much that the ncrease n dosyncratc rsk exposure at the loan level on average more than offsets the ncrease n loan numbers. The paper then turns to modelng the effects of ths change n equlbrum lendng behavor on real actvty. Naturally, more fundng for projects wth dosyncratc returns mples that the correlaton between projects wll lkely declne over tme, consstent wth the emprcal fndng of fallng covarance across frms and ndustres over the past few decades. More subtly, greater dosyncratc volatlty on the fnancal sde may n fact concde wth lower volatlty largely dosyncratc volatlty of real varables at the frm level. The fallng rsk premum on the dosyncratc rsk of borrowng frms cash flows has the mplcaton that frms wll fnd t optmal to place more weght on smoothng output and less on smoothng cash flows. Frms have a standard producton-smoothng motve n the face of demand shocks because of convex producton costs. Frms also have an ncentve to smooth cash flows because, lke banks, they too face a convex cost of external funds due to asymmetrc nformaton problems. To the extent that nventores rse when future sales and thus revenue are expected to exceed the current level, and so nventory accumulaton needs to be funded by borrowng, frms have to optmally trade off these two smoothng needs. Wth a lower margnal cost of external fnancng, especally dmnshng penalty for frm-specfc cash flow fluctuatons, frms wll fnd t optmal to allow more producton smoothng and accept more volatle cash flows as a consequence. 3

5 As a result, we are lkely to observe that real varables such as output, employment and nvestment become less volatle, even whle fnancal varables such as cash flow and the demand for external funds net debt or equty ssues become more volatle. Ths predcton s consstent wth the macro evdence that the volatlty of aggregate output and ts components has declned, whereas the volatlty of aggregate fnancal varables such as the amount of debt outstandng has mostly ncreased. It can also explan why frm-level employment volatlty has declned for the overall populaton of frms, whch comprses mostly prvate frms that rely on fnancal ntermedares for credt. The observed volatlty ncrease n publc frms, on the other hand, s lkely to be the result of changes n the selecton mechansm whch frms can and do choose to go publc. In summary, ths study shows that a sngle mechansm technologcal advances and nnovatons n the fnancal sector conssted of both ntermedares and those nsttutons that make the markets can lnk the mosac of stylzed facts of trends n aggregate vs. frm-level volatlty, volatlty of real vs. fnancal varables, and the changng mportance of systematc relatve to dosyncratc rsk. Its proposed explanaton s especally applcable to prvate frms, whch consttute the majorty of the frm populaton. The deal data for emprcally testng the model s predctons would be matched bank-borrower data on both producton and fnancal varables. Data on prvate frms would be especally nformatve. Such data not beng avalable, ths paper provdes a varety of evdence from the fnancal markets n support of ts hypothess. The paper s organzed as follows. Secton I brefly revews the set of relevant emprcal fndngs and how they relate to one another accordng to the model presented here. Secton II spells out how ntermedares lendng behavor should change n response to ICT advances and the mpled trend of ther portfolo dversfcaton, and then reports the actual trend. Secton III shows the mplcatons for nonfnancal frms real and fnancal actvtes and how they are consstent wth the exstng emprcal evdence. Secton IV concludes and dscusses extensons. 4

6 I. Solvng A Jgsaw Puzzle One of the most strkng features of economc fluctuatons n the U.S. n the past thrty years has been the notceable declne n volatlty around md 980s. In partcular, the standard devaton of GDP growth s about one thrd lower snce 984 than t was durng 960 to Km and Nelson (999) and McConnell and Perez-Quros (2000) frst dentfy the break date to be 984. Ths declne n volatlty s wdespread across sectors as well as the U.S. states (e.g., Owyang, Pger and Wall, 2006). Smlar declnes n aggregate volatlty are also found n the other developed countres, although the tmng and exact features dffer across countres. (See Stock and Watson 2003 for a summary). The ntal evdence at the frm level, however, seems to ndcate a contrary trend. For example, usng accountng and stock market data of frms publcly trade n the U.S., Comn and Phlppon (2005) fnd that frm-specfc volatlty n terms of sales, earnngs, employment, and captal expendture has been trendng up snce 960. At the same tme, fnance studes have also fnd an upward trend n the frmspecfc volatlty of stock returns (e.g., Campbell et al. 200). Increased share of dosyncratc volatlty mples decreased correlaton across frms. Furthermore, Campbell and Taksler (2003) document a concurrent rse n the corporate-treasury bond yeld spreads. They show that the yeld spread of a corporate bond rses n the dosyncratc rsk of the frm s stock, whch n fact has nearly as much explanatory power as credt ratng. For frm-level volatlty to rse and yet aggregate volatlty to fall, the covarance between frms obvously must declne. That s exactly what Irvne and Schuh (2005) fnd usng ndustry data. They dscover that average covarance of output growth across fnely classfed ndustres has declned, and surmse that t s the result of the ncreasng role of nventores as buffer stock. Comn and Phlppon (2005) also note that, between 959 and 996, there has been a declne n the covarance of growth across sectors for value added per worker and TFP. A new twst to the story, however, has just surfaced. Usng employment data of not only the 3 Blanchard and Smon (200), on the other hand, argue that a downward trend n economc volatlty started as early as the 950s and was nterrupted n the 970s and 80s. 5

7 publcly traded frms but vrtually all the prvate frms, Davs et al. (2006) fnd that frm-level employment volatlty has n fact declned n the prvate frms, as has the aggregate volatlty. Ths suggests an explanaton for the declne n aggregate output volatlty wthout resortng to lower covarances. But Davs et al. (2006) also confrm an ncrease of volatlty n the publc frms, as found by Comn and Phlppon (2005). They speculate that the dvergng trends n employment volatlty between publc and prvate frms may be due to changes n the selecton crtera of publc frms. These peces of emprcal facts seemngly contradctory at tmes add up to a sort of jgsaw puzzle and have, not surprsngly, attracted much research nterest. Early attempts to explan the great moderaton n aggregate volatlty focused prmarly on the role of mlder economc shocks and better monetary polcy, as well as changes n propagaton mechansms such as mprovements n nventory management technology (see Stock and Watson 2003 for a revew). Over tme, more attenton has been pad to another potental explanaton: ncreasng effcency of fnancal markets and nsttutons may have reduced shocks emanatng from the fnancal sector as well as moderated the propagaton of real shocks. For nstance, Dynan et al. (2005) explore possble lnks between fnancal nnovatons and the observed moderaton n economc actvty, and suggest that fnancal nnovatons should be added to the lst of lkely contrbutors to the ncreasng stablty snce md-980s. Fnancal development s also suggested as an explanaton of the ncrease n dosyncratc volatlty, and possbly a smultaneous decrease n aggregate volatlty. 4 Thesmar and Thoeng (2006) post that easer or cheaper access to fnancal markets facltates rsk sharng for the ndvdual entrepreneur so that dosyncratc volatlty becomes less costly n utlty terms, and ths spurs entrepreneurs to adopt more rsky technologes and thus leads to greater frm-specfc volatlty. Recently Jermann and Quadrn (2006) suggest that greater fnancal flexblty, defned as frms ablty to substtute between external debt and equty ssues, can n fact lead to hgher volatlty of fnancal 4 Addtonal canddates proposed to explan the volatlty trends nclude endogenous technology growth and ncreased competton. Comn and Mulan (2005) presents a model n whch frms choose the relatve resource allocaton between two types of R&D actvtes that jontly determne dosyncratc and aggregate volatlty of technology growth. Phlppon (2003) and Gaspar and Massa (2004) explan the ncrease n dosyncratc volatlty as a result of rsng competton n product markets. 6

8 varables whle effectng lower volatlty of real varables. Both of these arguments, however, are relevant only for publcly traded frms, not the majorty of frms, whch are prvate and relatvely small. Morgan, Rme and Strahan (2004), on the other hand, provde some evdence that better dversfcaton on banks part, through nterstate bankng, leads to lower volatlty of employment at the state level. But they do not dstngush between volatlty of real and fnancal varables, nor between dosyncratc and aggregate volatlty. Lke these prevous studes, ths paper also proposes developments n the fnancal sector as an explanaton, but for both the jont evoluton of frm-specfc vs. aggregate volatlty and the possble dvergence between the volatlty trends of real and fnancal varables. Its value added to the lterature les prmarly n ts ablty to consstently explan the varety of volatlty trends usng a unfed, technology-based mechansm that s relevant for the majorty of frms. Ths s acheved by hghlghtng the technologcal evoluton n fnancal ntermedares, on whom most frms rely for credt. Table summarzes the stylzed facts ths study seeks to explan. It organzes the relevant prce and quantty varables nto two categores: real (such as output, nvestment and employment) vs. fnancal (such as dvdends, net borrowng and equty ssuance). 5 All trends concern the growth rate. The model developed here manly tres to explan two trend patterns. Frst, the volatlty of fnancal quanttes seems to have trended up even whle the volatlty of real quanttes has trended down. For example, Fgure depcts the 5-year tralng standard devaton of the 4-quarter growth of net borrowng by nonfarm corporate busness. It dsplays an upward trend snce early 970s and especally n the 90s. Moreover, volatlty trends for real and fnancal quanttes seem to dverge at both the frm and aggregate level. Second, correlaton and even covarance across frms have declned for most varables, ndcatng the growng mportance of dosyncratc volatlty. 5 Note that the fnancal varables n the table concern rsky nstruments ssued by the prvate sector, not credt-rskfree Treasurys. Ths dstncton s mportant, because the volatlty of Treasury yelds has n fact declned, n large part because nflaton has become much less volatle (Stock and Watson, 2003). In contrast, the volatlty of stock ndex returns has not trended down (Campbell et al. 200). The reason lkely les n the volatlty of rsk premum. At monthly or even annual frequency, rsk premum s an order of magntude more volatle than the credt-rsk-free rates and thus domnates the return volatlty. 7

9 The model traces the root cause for both observatons to cheaper and better computng and communcatons technology (popularly referred to as ICT), whch enables fnancal nsttutons to process all types of nformaton more effcently, be t credt nformaton or smple fund transfers. Fnancal frms top the lst of benefcares of ICT mprovements because nformaton processng s at the core of ther operaton, as evdenced by ther heavy nvestment n ICT. As Inklaar et al. (2005) show (n ther Table 3), the contrbuton of ICT deepenng to productvty growth s nearly fve tmes hgher n the fnancal sector than n the ICT ndustry tself and more than two tmes hgher than n busness servces. Advances n ICT has substantally lowered (both margnal and average) cost of external fnancng, especally for small frms and households. The cost reducton s partly effected through greater competton among fnancal nsttutons, as ICT has enabled the processng of many types of fnancal nformaton to be standardzed. The lower margnal fundng cost allows small borrowers to tolerate more volatle cash flows and acheve greater producton smoothng. Ths s because the small borrowers lkely face convex cost for external funds, n addton to the usual convex cost for producton. They thus must trade off the need to smooth the amount of borrowng vs. producton. 6 Ths s the mechansm underlyng the dvergent trends between real and fnancal quanttes. 7 It should be noted that the predcted ncrease n cash flow volatlty should be nterpreted as relatve to the volatlty of demand. Ths means that, f each frm s sales become suffcently less volatle over tme, then the volatlty of ts cash flows can n fact declne as well, but by less. Furthermore, lendng to a larger number of smaller borrowers boosts a portfolo s dversfcaton, reducng the premum on dosyncratc rsk. In addton, ICT has both enabled and stmulated fnancal nnovatons, such as new fnancal contracts (.e., securtes, such as dervatves) along wth new markets for ther tradng. These nnovatons enhance rsk sharng and thus further lower the premum on 6 An ncentve to smooth borrowng lkely translates nto an ncentve to smooth cash flows, as long as fundng needs, for captal and nventory nvestment, are not perfectly correlated wth cash flows. 7 Ths model does not explctly consder fnancal frctons n the form of quantty constrants. The combnaton of greater volatlty of fnancal quanttes wth lttle trend n market return volatlty n Table can plausbly be nterpreted as the effect of less quantty restrctons owng to fnancal development. Snce the supply of loanable funds s lkely to be qute elastc, t determnes the volatlty of the rate of returns, whle demand varatons determne the volatlty of quantty. 8

10 dosyncratc rsk. Ths change n the relatve prce of components of rsk underles the growng mportance of dosyncratc volatlty. Combnng the above two predctons mples that the predcted ncrease n cash flow volatlty should be accounted for mostly by dosyncratc rsk. By the same token, the quantty of a narrowly defned type of fnancal nstrument s lkely to become more volatle relatve to the sum across multple types, as fnancal markets become better ntegrated and credt restrctons less bndng. That s, buyers of funds can more freely dversfy across dfferent nstruments to mnmze the cost of external funds. Note that, n terms of the mpact of ICT on operatng effcency, ntermedares and markets are modeled qualtatvely the same n ths study. It s reasonable to hypothesze that ICT advancement has also boosted the productvty of the fnancal nsttutons that organze the markets. On the other hand, ntermedares and markets have dfference comparatve advantages that lead them to specalze n processng dfferent knds of nformaton and servng dfferent knds of borrowers and nvestors. Ths paper shows how the combnaton of ntermedares and markets enables households and most frms to stll beneft from nnovatons n the markets, even though drect access to fnancal markets s prohbtvely expensve for these agents. Ths paper proposes that ntermedares such as banks serve as a condut between markets and those small borrowers. Banks specalze n processng the credt nformaton of a large number of small scale projects, and then pool loans of smlar attrbutes to mnmze dosyncratc rsk. They then access fnancal markets, whch n turn dversfy away ntermedary-specfc rsk. The cost savngs enjoyed by ntermedares owng to more effcent markets wll most lkely be passed on to the prvate borrowers, who thus beneft ndrectly. In fact, households and prvate frms nowadays can even drectly share n such cost savngs because the rapd growth of secondary markets for loans means that many loan pools are securtzed and drectly held by market nvestors, whle banks contnue to specalze n servcng small accounts. Small frms better ntermedated access to markets s evdenced by the fact that the external debt balance of nonfarm noncorporate busness has become almost perfectly correlated wth that of nonfarm nonfnancal corporate busness (Fgure 2). 9

11 Drect testng of the predctons of ths model requres matched bank-borrower data. It not beng avalable, the emprcal secton of ths paper resorts to a varety of ndrect evdence, n partcular the ncreasng share of dosyncratc rsk n banks asset portfolos. The valdty of such a test rests upon a symmetry argument between banks and ther borrowers. If banks rase the dosyncratc volatlty of ther fnancal return n response to more effcent dversfcaton of dosyncratc rsk n the markets, then optmzng frms should behave lkewse n response to better dversfcaton n banks portfolos. The next secton develops the fnancal sde of the model, showng how the composton of rsk changes n response to better technology and how frm s and bank s volatlty evolve jontly. II. Fnancal Intermedaton Technology and the Optmal Loan Interest Rate Ths secton detals how the optmal debt or loan nterest rate charged, the average sze of loans made, and the rsk composton of loan portfolos evolve n response to advances n ICT. Here I adopt the costly-state-verfcaton framework a la Townsend (979), n whch case ntermedares rasons d être s to resolve borrowers prvate nformaton. 8 For clarty of exposton, I assume that ntermedares possess a montorng technology that enables them to resolve the nformaton asymmetry fully. 9 Ths can be vewed as the lmtng case for the capablty of lendng technology. It must be emphaszed up front that, although the analyss s specfed n the context of nonfnancal frms borrowng from banks, the logc s vrtually the same for the case of banks (as well as nonfnancal frms) borrowng n the publc markets. In publc debt markets, the counterpart to banks ntermedary that resolves nformaton problems s the credt ratng agences. Most mportantly, the key concluson that better lendng technology and the ensung greater dversfcaton leads to lower prce of dosyncratc rsk also apples to the publc debt ssued by banks. Ths n turn has mportant mplcatons for banks borrowers as well: t helps further lower the prce of credt to them. 8 Addng screenng by banks wll not change any of the propertes of the lendng technology consdered here. For detals, see Wang, Basu and Fernald (2004). 9 I also do not analyze the optmal contract ssue and only consder determnstc montorng, whch can be the optmal contract f commtment s lmted, see Krasa and Vllaml (2000). 0

12 sze as Assume that borrower has one contnuously scalable project n perod t, and denote the project s K t. The borrower may put up her own wealth (denoted W t ) to fnance part of the project and borrow the rest (.e., K t Wt ). Assume the project s gross return, denoted t R +, s non-negatve. 0 A loan s deemed n default f, at the end of perod t, the borrower s return falls short of the requred nterest payment,.e., ˆ ( R ) t+ Kt < Zt+ Kt Wt, where Z ˆ t + s loan s promsed yeld (.e., nterest rate specfed n the contract that the borrower would pay f solvent), and R t + s a realzed value of return. So, for gven W t, there s a one-to-one mappng between ˆ t Z + and a threshold value of R t + (denoted R t +, and agan ˆ note that t s known at tme t, despte ts tme subscrpt), below whch loan s consdered n default: Rˆ = [ Zˆ ( K W )] K = Zˆ k, ( ) t+ t+ t t t t+ t where k = ( K W ) K s borrower s debt-to-asset rato (.e., leverage). ( ) shows ntutvely that, t t t t ˆ for any gven Z t +, hgher leverage rases a borrower s odds of default (.e., a hgher k t leads to a hgher ˆ t R + ). To make further dervatons more tractable, we now assume that the value of the project/frm follows a standard geometrc random walk, and so r = ln( R ) = ln( K ) ln( K ) = α + ξ, ( 2) t+ t+ t+ t t+ where α s the postve drft of the process, and ξ t + s the nnovaton. Defne the default ndcator d t + = f the frm defaults (.e., ˆ r ˆ t+ < rt+ = ln( Rt+ ) ), and 0 otherwse. When default occurs, the lender montors (or, more precsely, audts) the borrower to fnd out the project s true resdual value. Ths actvty s qualtatvely smlar to producng other nformaton servces such as consultng and accountng. It ncurs resource cost, such as to hre labor and purchase captal and 0 The subscrpt of R t + sgnfes that t s not known untl the end of perod t (= the begnnng of t+). In general, tme subscrpts n ths paper denote the perod when the varable s value becomes known, unless noted otherwse. Even though Z ˆ t + s contracted and thus known at the begnnng of t, we keep the (t+) subscrpt to sgnfy ts connecton wth R t +, when t becomes known whether Z ˆ + can be met. t

13 materals. Denote the (margnal) cost of montorng a loan as υt ( Λ ), where Λ s the vector of relatve loan characterstcs (e.g., sze, borrower s ndustry and repayment hstory, etc.). Ths margnal cost s most lkely concave n loan sze, snce, ntutvely, a $2 mllon loan unlkely requres twce as much processng as a $ mllon loan. (See Wang, Basu and Fernald 2004 and Wang 2003a, for more n-depth dscusson of the propertes of banks technology for processng nformaton.) For smplcty, consder the case where υt ( ) s only a functon of loan sze (.e., Λ s a scalar), and assume υ t 0 whle υ t 0. A smple example would be υ ( K W ) = a + b( K W ). t t t t t t t Then the lender s rate of return on loan can be expressed as 2 υ t υ + t+ z ˆ ˆ t+ = ln( Zt+ ) mn{ rt+, rt } ln kt rt dt rt ( dt ) ln k + = t. ( 3) KR t t+ KR t t+ Clearly, both z t + and d t + are random varables, and the expected default probablty s r ˆ t+ μ prob( d t + =) = E t ( d t + ) d t + = prob( r ˆ t+ < rt+ ) = Φ r, ( 4) σ r f assumng the project s return follows a normal dstrbuton. Φ(.) s the c.d.f. of the standard normal, and E t (.) denotes the expectaton condtonal on the nformaton set at t. μ r and σ r are the mean and standard devaton of the project s return, respectvely. Then the rate of return the lender expects to receve on loan s υ t E t ( z t + ) = E t r + ˆ t+ dt rt ( dt ) ln k t. ( 5) KR t t+ Intutvely, that the overall expected return on a loan depends on not only the default probablty but also the recovery rate n case of default. 2 In levels, the lender s return equals υ t ˆ Kt R + t+ dt Rt ( dt ) Takng log and smplfyng wth KR t t+ υt the relatonshp ln KR payoff under default. υ + t+ t t+ KR t t+ assumng the montorng cost s small relatve to the project s total 2

14 Denote the expected rate of return requred by a lender on loan as μ t + (known n perod t). For a perfectly dversfed lender, μ t + depends only on loan s systematc rsk, whch stems from the correlaton between the systematc factors and s default event (.e., d t + ) as well as ts recovery rate. 3 However, for less than fully dversfed portfolos, rsk-averse lenders also demand compensaton for unexpected losses, whch can be substantal. (See Amato and Remolona 2003 for a detaled dscusson of how the dffculty of dversfyng debt portfolos, due to the extreme skewness of debt return dstrbuton, may explan the corporate-treasury bond spreads, whch seem unreasonably wde n general.) The equlbrum condton that determnes the nterest rate on a debt s μ t + = E t ( t υ t z + ) = E t r + ˆ t+ dt rt ( dt ) ln k t. ( 6) KR t t+ Obvously, the promsed yeld z ˆ t + rses n the requred return μ t +, snce zˆ = = = > 0. ( 7) μ t+ ˆ t+ E( t zt+ ) zˆ t+ E( t zt+ ) rt+ dt+ Ths s the condton that underles the evoluton toward greater exposure to dosyncratc rsk n borrowers cash flows and n turn banks loan portfolos: a relatvely lower premum on dosyncratc rsk confers a cost advantage to borrowers wth greater specfc rsk and n turn reduces the cost of funds n general. Gven μ t +, the montorng cost leads to a hgher promsed yeld: zˆ t d + t+ = E t ( t ) 0 d + >. ( 8) υt+ KR t t+ The montorng cost s the element that truly drves a wedge ex ante between the cost of external and nternal funds. As better technology lowers lenders margnal cost of processng an extra borrower s credt nformaton, the wedge should shrnk. 3 Accordng to the poneerng analyss of corporate debt prcng by Merton (974), the rate of return on a company s bond should be perfectly correlated wth that on ts equty. In the CAPM context, ths requres that a corporate bond s market beta normalzed by ts dosyncratc volatlty equals the correspondng stock s market beta normalzed by ts dosyncratc volatlty. 3

15 The promsed yeld also rses wth a borrower s leverage: 4 ( υ ) k +E d R = > > 0. ( 9) ˆ t z t t t t t+ kt kt E( t zt+ ) zˆ t+ dt+ The second term n the numerator stems from the fact that, for a project of gven sze, hgher leverage means a larger loan balance and thus montorng cost n expectaton snce υ + > 0. Hence, the more a project borrows, the hgher the nterest rate t has to promse. Ths establshes the case of a convex borrowng cost, whch s by now a common assumpton made n models of fnancal frctons, such as Froot, Scharfsten and Sten (997) and Bernanke, Gertler and Glchrst (998). For a borrower wth a gven scale of operaton, z ˆ t+ kt s equvalent to the margnal cost of extra borrowng. Clearly, ths margnal cost rses n υ t + the extra cost for the lender to process a margnally larger loan snce t zˆ k υ > 0. (0) t+ t t+ We wll see that t s condton (0) that leads to fallng margnal cost of funds, gvng each borrower ncentve to allow more fluctuatons n cash flows and n turn the amount of borrowng, and consequently acheve greater smoothng of real output. Note the dfferent effect of a fallng υ t + vs. that of a fallng premum on dosyncratc rsk on the cost of funds. The former lowers a borrower s margnal cost of funds regardless of the nature of her cash flow volatlty whereas the latter s only for dosyncratc volatlty. υ t + On the other hand, gven the leverage rato () s strctly concave: k t, the promsed yeld falls wth a loan s balance f zˆ t υ t υ t υ t υ t+ = E t =E 2 t < 0. ( ) ( Kt Wt ) KR t t+ ( Kt) R t+ KR t t+ υt+ K t 4 The montorng cost lkely also rses n a borrower s leverage, and that wll make the promsed yeld ncrease even faster wth leverage. 4

16 Ths s because, gven the concavty assumpton, the extra cost of montorng a margnally bgger loan wll not exceed the average cost, and so υ υ K < 0. If montorng even a small loan nvolves a t+ t+ t fxed cost that s greater than the extra cost of montorng a margnally bgger loan,.e., υ ( ) υ ( ) < 0 for a small postve, then the margnal cost wll asymptote to the average from t+ t+ below. More mportantly, as the cost of montorng an extra loan falls regardless of loan sze (e.g., a n υ t + Kt Wt at + bt + Kt Wt ( ) = + ( )), small loans beneft more n the sense that ther promsed nterest rates fall more than large loans rates: zˆ t+ = Et 0 2 <. ( 2) ( Kt Wt ) υt+ ( Kt) Rt+ Ths mples that, f advances n lendng technology manfest more n lowerng the per-loan margnal cost regardless of loan sze, then t has the drect effect that every bank makes more loans of smaller sze on average, snce more projects now qualfy, assumng the same dstrbuton of project returns. In fact, banks wll seek to merge n order to take advantage of the greater ncreasng returns to scale. Ths s consstent wth the merger wave observed between the md 980s and late 990s. More mportantly, most of the addtons to the loan pool are small loans. 5 Now consder the ensung ndrect effect of technologcal advances on the rsk composton of bank loan portfolos. All of the above analyss assumes a constant expected rate of return requred by a lender. But the determnaton of the requred rate of return on a margnal loan changes as a loan portfolo becomes better dversfed. Greater dversfcaton means that each addtonal loan s dosyncratc rsk matters less to the resultng new portfolo s volatlty, whch n the lmt wll be entrely determned by the systematc rsk of the consttuent loans. Ths ndrect effect can be llustrated by gvng more structure to the shocks to a project s return 5 A lkely general equlbrum effect s that, as captal ntensty rses owng to more net nvestment, margnal product of captal falls and thus the new projects funded wll eventually have lower average rate of return as well. 5

17 ( t ξ + ). Assume ξ t + has the followng mult-factor structure: ξ = β m + σ, wth t +..d.(0, ). ( 3) t+ t+ t+ m t+ s an m vector of systematc factors (such as GDP growth, rsk-free nterest rate, etc.), whle β s the vector of s factor loadngs. t + s the..d. frm-specfc shock, wth standard devaton σ. m m Assume mt+ N( μ t+, Σ t+ ), then r t + has mean + βμ m 2 and varance σ = βσ β + σ. μ r = α m t+ 2 r t+ βσ m t+ β and 2 σ measure the sze of the systematc and the dosyncratc rsk, respectvely. In ths setup, the requred rate of return rses n σ,.e., μt+ σ > 0, but the ncrease decelerates n a portfolo s degree of dversfcaton. Ths can be shown by recognzng that, n general, total rsk of each loan s return can be decomposed as var( z ) = E [var( z m )] + var [E( z m )]. t+ m t+ t+ m t+ t+ And the varance of loan s return condtonal on the systematc factors s bounded: r υ K R var m( z ) ( r ) var d 2 t+ t+ t t+ ˆ t+ mt+ = t+ t+ mt+ rˆ t+ { m ϕ m m ϕ m } { m ϕ m m ϕ m } = ( rˆ ) E [( d ) ] [E ( d )] t+ t+ t+ t+ t+ t+ t+ ( rˆ ) E ( d ) [E ( d )] ( rˆ ) t+ t+ t+ t+ t+ t+ t+ t+ ϕ r υ K R (0,) s the fracton of loss for the lender gven a loan s default, and so t+ t+ t t+ t+ ϕ t+ rˆ t+ ϕ t + (0,) and ( ϕ d ) ϕ d. Therefore, as N, 2 t+ t+ t+ t+ 2 2 E [var( Z N N, ˆ )] E ( w ) var ( z ) Nt t t t t ( t t ) 0 4 wr m + m + = m = + + = + m m, snce, condtonal on the systematc factors, the dosyncratc returns are ndependent. 6 w t s the portfolo weght of loan, and N the number of loans n the portfolo. 6 N 2 When a portfolo s less well dversfed, ts return varance rses n ( ) N 2 w. lm ( ) 0 j= w t t = under the N 2 granularty condton ( w ) = O ( N ), so n the lmt weght dstrbuton of ndvdual loans no longer matters j= t N j= 6

18 Therefore, as a portfolo becomes more dversfed, ts return varance becomes domnated by varatons of the systematc factors: { m m } { m } lm var( Z ) = lm E [var( Z m )] + var [E( Z m )] = lm var [E( Z m )]. Nt, + Nt, + t+ Nt, + t+ Nt, + t+ N N N That s, a portfolo s total rsk asymptotes to ts systematc rsk, whch stems entrely from ndvdual loans return correlaton wth the systematc factors. Hence, n the lmt N, μt+ σ =0. Jarrow, Lando and Yu (2005) also show that, under certan condtons that permt the constructon of dversfed portfolos, the default of any partcular frm wll not command a rsk premum. The mplcaton s that, as a portfolo becomes suffcently dversfed, loans wth low systematc rsk would face relatvely lower μ t + and thus pay lower nterest rates (see equaton ( 7)), regardless of ther dosyncratc rsk. Ths means, as more and smaller loans are added to a portfolo, projects whose return varatons are accounted for more by dosyncratc rsk wll face a lower borrowng cost. Thus, even gven the dstrbuton of loan-level systematc vs. dosyncratc rsk composton, the share of loans that have greater dosyncratc volatlty wll rse n loan portfolos n the new equlbrum. As mentoned n the begnnng of ths secton, the exact same logc apples to banks borrowng n the publc debt markets as well. As nvestors n the debt markets become better dversfed, they demand lower premum on the bank-specfc rsk of each debt ssue. As a result, all else equal, the cost of external funds wll fall for banks whose return varance s more accounted for by dosyncratc rsk. The forces underlyng market nvestors ablty to better dversfy are essentally the same as those that enable banks to dversfy, namely ICT and fnancal nnovatons, whch make t possble for fnancal nsttutons servng the markets to provde funds more cheaply. The relatonshp between bank-specfc and loan-specfc rsk can be llustrated usng the smple for portfolo rsk. For example, under the Vascek (99) model, for a portfolo conssted of loans wth dentcal * * N d ( d ) ρ + ( ρ ) ( w ) 2, where ρ * s the correlaton return dstrbuton, the varance of ts loss equals t t { j= t } between any two loans defaultng, all condtonal on perod t s nformaton, ncludng the outcome of the systematc factors. If two projects returns follow a jont normal dstrbuton, then ther default correlaton 2 * Φ2 [ Φ ( dt), Φ ( dt), ρ] dt ρ ( dt, ρ) =, where ρ s correlaton between the two projects returns. d ( d ) t t 7

19 CAPM model. Frst, a bank s asset return can be decomposed as r = β r +, (4) b m b t bm t t where b r t and m r t are the excess returns on bank b and the market portfolo, respectvely. b t s the bankspecfc return, orthogonal to m r t by constructon. The above analyss ndcates that, as market nvestors become better dversfed, the premum on the volatlty of t b wll declne and asymptote to zero,.e., b b μ σ 0. t Wthn each bank, the return of loan can be wrtten as r = β r + = β β r + β + = β r + β +, (5) b b b m b b m b b t b t t b bm t b t t m t b t t and r = wr, wth w b t = and w β b t b =. So, better dversfcaton for a bank s loan b b t b t t b portfolo s defned wth regard to loan-specfc volatlty t. There can stll be non-degenerate bank- b b specfc volatlty even when a bank becomes well dversfed and thus μ σ 0. And snce the b t t covarance between loans and j wthn the bank cov( r, r ) = β β ( σ ) + β β ( σ ), the loans b jb m 2 b 2 t t m jm b jb covarance wth the bank-wde shocks wll stll command a rsk premum (.e., β b does not asymptote to zero). 7 b b It s only wth market nvestors better dversfcaton wll μ σ 0. t Ths wll nduce banks to choose a hgher σ β σ + σ, and possbly even a hgher b 2 2 m 2 b 2 ( ) [ bm( ) ( ) ] b σ b b n level. If at the same tme σ rses suffcently relatve to σ (that s, enough to offset the declne n the cross-loan average b 2 2 b 2 b 2 ( σ ) [ βb( σ ) ( σ ) ] + as the number of loans n a portfolo grows), then the dversfcaton across loans wthn the bank can fall as well. 8 By comparson, a lower correlaton wth the market return at the portfolo level automatcally means that ndvdual loans are now less correlated 7 Note that the dervaton here s more statstcal than causal, n that t does not address the causalty of b t whether t s the non-market comovement among the bank s loans or shocks ntated by the bank. 8 It s also possble that a lower correlaton wth the market return at the portfolo level concdes wth a hgher 2 dversfcaton across loans wthn the bank f ( b 2 βbβ jb σ ) exceeds ( σ b ), whch can arse f a bank chooses to orgnate loans wth smlar attrbutes. But ths outcome s much less lkely gven the observed evoluton of bank portfolos. 8

20 wth the market as well, that s, a lower b 2 2 m 2 b 2 ( σ ) [ βbm( σ ) ( σ ) ] + mples a lower σ β σ + σ. b 2 2 m 2 b 2 ( ) [ m( ) ( ) ] b b The savng on banks cost of funds as μ σ 0 wll be passed on to ther borrowers, at least t partly, snce t seems unlkely that ndvdual banks market power n the loan market has ncreased enough to fully offset t. So, the key concluson to draw from (4) plus (5) s that lower fnancng costs, n large part owng to lower premum on dosyncratc rsk, that stem from fnancal market developments can beneft even frms that do not or cannot access the markets. The savngs are passed on to such prvate frms through fnancal ntermedares such as commercal banks, whch have better access to the markets. Next we dscuss an mportant ndrect effect of a fallng premum on dosyncratc rsk relatve to that on systematc rsk on the rsk composton of borrowers cash flows. Ths change n the relatve premum s essentally a change n relatve prces nvestors are wllng to pay for debt securtes of dfferent rsk attrbutes: less prce dscount on a debt f ts volatlty s more dosyncratc. Thus, sellers of debt securtes (vz. borrowers) naturally react by offerng more debt characterzed by dosyncratc rsk. The mplcaton for borrowers operaton s that they should adopt strateges that lead to fluctuatons less correlated wth aggregate condtons. Only a weak condton on borrowers behavor s suffcent for the above argument to hold: the tradeoff between return and total rsk has not changed as much for each ndvdual borrower. So the operaton plan chosen by borrowers under the old lendng technology must generate postve surplus for them under the new technology. In response, they may even ncrease total project rsk n order to attan maxmum utlty. In fact, frms may prefer to assume greater dosyncratc rsk, n such forms as a narrower product lne, snce more concentraton may well allow more specalzed and thus effcent producton technology, as well as a better ft to the taste of the target market and hence hgher markups. Ths s bascally the dea of a core competency. In summary, borrowers optmal reacton to the relatve premum change wll further the compostonal change of loan portfolos n the new equlbrum, a bgger share of whch wll be accounted for by projects whose volatlty conssts more of dosyncratc rsk. 9

21 Note that the above reasonng of borrowers optmal reacton apples to any frm that seeks external funds, whch ncludes banks themselves. Ths means that, even as a bank s portfolo becomes better dversfed so that average loan-specfc volatlty (.e., b ( σ ) w b t 2 ) declnes, bank-specfc rsk b σ may account for a bgger share of total bank return volatlty. Nonetheless, f the correlaton across loans wthn a bank wll stll declne. b σ rses relatve to Furthermore, f the new technology allows not only nvestors but also borrowers to attan better rsk sharng, then t wll lkely gve borrowers addtonal ncentve to rase just the project-specfc rsk. The reason s straghtforward: f borrowers can dversfy away more of the project-specfc return volatlty through nsurance and other contracts, and f a project s mean return rses wth ts total rsk ncludng the dosyncratc rsk then the borrowers wll want to ncrease the project-specfc rsk because the margnal beneft (.e., ncremental mean return) exceeds the margnal cost (.e., utlty loss). 9 Ths s essentally the mechansm studed n Thesmar and Thoeng (2006). The model s mplcaton for the degree of dversfcaton n fnancal ntermedares loan portfolos s detaled n Appendx. The goal s to formulate ndrect emprcal tests of the model by checkng whether changes n fnancal ntermedares dversfcaton over tme are consstent wth the model s predctons. Ths s a second best soluton gven the data lmtatons. A drect test of the model s not feasble, snce t would call for observatons of matched bank and borrower-loan data. b σ, II.2 Emprcal Analyss A. Tme Seres of Bank Rsk Decomposton and Testng of Model Predctons As explaned above, one of the model s predctons s that, for a fnancal ntermedary of a gven sze, ts degree of dversfcaton s lkely to have fallen as the effcent scale of operaton has rsen over the past two decades or so. To test these predctons, we estmate equatons of the followng structure: t, = + 0t+ At, + 2 t A t, + γ Zt, + t, ln( σ ) α β β ln( ) β ln( ). (6) 9 Snce the borrowers (especally those small frms, whch are often operated by owners) are lkely to be less dversfed than the lenders, total rsk but not just systematc rsk matters for ther welfare. 20

22 The dependent varable σ,t s a measure of the degree of dversfcaton for ntermedary n perod t. For comparson, I also regress the systematc, dosyncratc and total rsk. α s the fxed-effects term, to capture all the unobserved ntermedary-specfc characterstcs that may affect ts rsk propertes. t s a tme trend, and A,t- s the real sze of s portfolo at the begnnng of the perod. Z,t s a vector of control varables that n theory can also affect an ntermedary s rsk characterstcs, and they wll be dscussed later n greater detal. The null hypothess accordng to the model then s β 2 < 0, wth or wthout separate log assets and tme trend terms, when the dependent varable σ,t measures the degree of dversfcaton. (β 2 s expected to be more negatve wth the other two terms.) If the nteracton term s omtted, the sgn of β 0 s ambguous, snce BHC sze has grown substantally and so the average level of dversfcaton could have rsen over the sample perod. Wthout the nteracton term, β > 0 s expected, snce theory would suggest, and prevous research has provded ndrect evdence, that the share of systematc rsk s generally hgher for larger frms. 20 When σ,t measures dosyncratc rsk, β 2 s agan expected to be negatve. The hypothess s that, owng to cheaper and better ICT, t s now proftable for banks to make smaller loans. Thus a gven dollar volume now corresponds to a larger number of loans, most lkely leadng to smaller dosyncratc rsk, and so β 2 < 0. Wthout the nteracton term, β 0 s expected to be negatve as well whle β postve. The sgns of these coeffcents are less clear when σ,t measures total and systematc rsk. It s worth notng that, f the effect from decreasng average sze of loans s strong enough, t can n fact domnate the effect from new assets greater dosyncratc rsk and result n ncreasng degrees of dversfcaton over tme. Therefore, the coeffcents from regressons of the rsk components together wth that from the regresson of dversfcaton can offer clues to the lkely mechansms that have brought about the changes n BHCs rsk composton. If we see decreasng dosyncratc rsk along wth nonncreasng (.e., negatve or nsgnfcant β 2 ) dversfcaton, then t s most lkely that the new assets 20 For example, Demsetz and Strahan (997) found that dosyncratc rsk s lower for larger BHCs. 2

23 added to bank portfolos over tme are subject to greater proportons of dosyncratc rsk. The systematc rsk must be declnng as well n ths case, and so thus so does total rsk. The fnancal ntermedares consdered n ths model mostly correspond to banks and bank holdng companes n the real world. They lend to prvate and mostly small frms, whch do not or cannot obtan fundng from the markets. 2 Snce hgh frequency return data necessary for estmatng the change n rsk s only avalable for publc frms, our sample s all the publcly traded bank holdng companes. The rsk measures used n the estmaton of (6) are based on monthly stock returns. To obtan the dependent varables n (6), we decompose return varance accordng to asset prcng models. That s, we frst estmate an asset prcng equaton such as the CAPM, and take the ftted values as a measure of the securty s systematc returns, and the resduals a measure of ts dosyncratc returns. Standard devatons of total rate of return on the stock and ts two components then measure the total, systematc and dosyncratc rsk, respectvely. The degree of dversfcaton s measured as the unadjusted R 2 from the asset prcng regressons, whch quantfes the fracton of a stock s return varaton that can be explaned by the systematc factors. For fnancal ntermedares, whch can be vewed as (actvely managed) portfolos of fnancal contracts, the R 2 statstcs can be nterpreted as measurng how dversfed the portfolos are. Four asset prcng models are consdered: the market model, the CAPM, and the CAPM augmented wth the two Fama-French factors (referred to as the FF model from here on), and the FF model further augmented wth one momentum factor (referred to as the momentum model from here on). Both the market model and the CAPM are famlar sngle-factor models. The Fama-French model augments the market factor n the CAPM wth two addtonal factors called HML (.e., hgh-mnus-low) and SMB (.e., small-mnus-bg). The momentum model further augments the FF model wth a momentum factor, to proxy for the momentum effects on stock returns as documented n Jagadeesh and Ttman (993). 2 Nowadays, there s a greater varety of fnancal nsttutons lendng to prvate and small busnesses, and a broader array of credt contracts. For example, credt card companes such as Amercan Express s routnely used by small busnesses for workng captals, and factorng has become wdely avalable as well. 22