The Term Structure of Money Market Spreads During the Financial Crisis

Transcription

1 The Term Srucure of Money Marke Spreads During he Financial Crisis Josephine M. Smih May 2012 Absrac I esimae a no-arbirage model of he erm srucure of money marke spreads during he recen financial crisis o idenify how much of he sharp movemens in spreads can be aribued o observable ineres rae, credi, and liquidiy facors. The resricions of he model imply ha longer-erm spreads are linear, risk-adjused expeced values of fuure shor-erm spreads. In addiion, he linear represenaion of spreads can be pariioned ino wo disinc componens: one relaed o ime-varying expecaions of spreads, and he second o ime-variaion in risk premia. Esimaion of he model highlighs he imporance of ime-variaion in risk premia. Up o 50% of he variaion of spreads is explained by ime-varying risk premia, and risk premia has significan predicive power for spreads. I am forever indebed o Monika Piazzesi and John Taylor, as well as Manuel Amador, Kahleen Easerbrook, Nir Jaimovich, Brian Kohler, Seve Kohlhagen, Yaniv Yedid Levi, Bijan Pajoohi, Marin Schneider, Johannes Sroebel, Edison Yu and seminar paricipans a BlackRock, Federal Reserve Bank of New York, Federal Reserve Bank of San Francisco, Federal Reserve Board, Harvard Business School, WashU Olin Business School, Sanford Universiy, NYU Sern School of Business, UBC Sauder, Universiy of Michigan, and Universiy of Washingon for useful commens. Financial suppor for his work was provided by he Shulz Graduae Suden Fellowship in Economic Policy and he Kohlhagen Graduae Fellowship a he Sanford Insiue for Economic Policy Research. Correspondence: Sern School of Business, New York Universiy, 44 Wes 4h Sree, New York, NY jsmih@sern.nyu.edu 1

2 Ineres rae spreads are a common measure of financial marke sress, and he recen financial crisis saw an unprecedened increase in boh he level and volailiy of spreads in a variey of markes. One paricular money marke spread receiving aenion has been he spread beween LIBOR and OIS raes of comparable mauriy, he LOIS spread. LIBOR raes are ineres raes for unsecured, longer-erm inerbank lending, while OIS raes are a measure of secured, shor-erm inerbank lending, ofen used as proxy for expecaions of fuure Federal Reserve policy. Figure 1 plos LOIS spreads a he one-, hree-, and welvemonh mauriies. Before he onse of he crisis, hese spreads were low and exhibied very lile ime variaion. However, Augus of 2007 saw a sharp increase in he LOIS spreads and hey have flucuaed well above hisorical averages since hen, rising o over 300 bps during he panic of The purpose of his paper is o decompose he observed ineres rae spreads ino wo disinc ye inerrelaed facors: credi and liquidiy. By credi, I am referring o he perceived increase in defaul probabiliies of financial insiuions who paricipae in he LIBOR survey, since counerparies wan o be compensaed for any losses ha migh occur in he even of defaul. By liquidiy, I am referring o he premium needed o enice invesors for illiquidiy, he fear ha asses in heir porfolios migh no be able o be raded easily and wihou significan price impac on oher asses. To do so, I esimae a fully-specified model of he LOIS erm srucure using he no-arbirage, affine models of Duffie and Singleon (1999) and Ang and Piazzesi (2003). These models build on he heory of he Expecaions Hypohesis (EH), in which longer-erm ineres raes are expecaions of fuure shor-erm ineres raes plus a consan erm premium. My model predics ha LOIS spreads are linear, risk-adjused expeced values of fuure shor-erm spreads: z (n) = a n + b T nx, (1) 2

3 3.5 3 One Monh LOIS Three Monh LOIS Twelve Monh LOIS 2.5 Percen / / / / / /2009 Figure 1: Weekly averages of daily daa of spreads beween LIBOR and OIS raes (LOIS spreads) a he one-, hree-, and welve-monh mauriies. where z (n) is he LOIS spread for mauriy n, X is he vecor of sae variables, and b n is a vecor of response coefficiens of he LOIS spread o he sae variables. The model assumes ha he sae vecor X follows a vecor auoregression (VAR), and hus he erm srucure in equaion (1) reduces o a VAR wih non-linear, cross-equaion resricions imposed by no-arbirage. The model delivers closed-form soluions for LOIS spreads as a funcion of he sae vecor X, and I can idenify how much of he spreads is due o each of he variables included in X. Specifically, I include hree differen variables in X : a benchmark inerbank ineres rae, a proxy for credi, and a proxy for liquidiy, all hree of which are enirely observable. This is 3

4 in conras o Dai and Singleon (2002), among ohers, which uses only laen variables in he sae vecor. Ang and Piazzesi (2003), Piazzesi (2005), Ang, Piazzesi, and Wei (2006), and Ang, Dong, and Piazzesi (2007) incorporae observable macroeconomic variables o replace laen facors and obain a beer fi of yield curve dynamics. A criical conribuion of he model comes from a pariion of he response coefficiens b n from equaion (1) ha separaes LOIS spreads ino wo componens. The firs is relaed o ime-varying expecaions of he fuure spread beween LIBOR and he Federal Funds rae, while he second is due o ime-variaion in risk premia caused by changes in risk aiudes of invesors. Since he model provides closed-form soluions for he separae componens, I can idenify how much of he movemens in spreads is direcly aribuable o each. Combining he VAR esimaion wih esimaes of risk premia, LOIS spreads reac mos sensiively o movemens in he credi facor. A subsanial proporion of he volailiy of spreads can be explained by risk premia (up o 50% for he welve-monh LOIS), and he response of spreads o shocks o X is mos sensiive o credi risk premia. To es he model, I examine he behavior of relaive excess reurns beween LIBOR and OIS, which my model predics are aribuable solely o ime-variaion in risk premia. Regressions of relaive excess reurns on he sae vecor X resul in a significan correlaions of boh he credi and liquidiy facors wih reurns, highlighing he imporance of ime-varying risk premia in explaining LOIS spreads. This paper relaes o recen empirical work ha has decomposed he increase in spreads such as Taylor and Williams (2008), McAndrews e.al. (2008), and Schwarz (2009). These papers use ordinary leas squares (OLS) regressions o aribue he rise in spreads o he same wo facors I concenrae on, credi and liquidiy. While he coefficien esimaes derived from OLS regressions of LOIS spreads on my measures of credi and liquidiy are comparable o he response coefficiens in equaion (1), here is no way o decompose 4

5 he OLS coefficien esimaes o idenify ime-variaion in risk premia. Anoher recen lieraure has developed ha incorporaes hese affine pricing ools in srucural general equilibrium models, including Bekaer e.al. (2005), Rudebusch and Wu (2007), Gallmeyer e.al. (2007), and Rudebusch and Swanson (2009). A full general equilibrium model would develop a srucural relaionship beween he macroeconomy, ineres rae spreads, and risk premia. However, he quesion I am asking is only relaed o an empirical explanaion of he erm srucure of LOIS spreads as a funcion of credi and liquidiy. The model has poenial implicaions for how policy can respond o money marke spreads. This is of ineres since mos of he non-radiional policy acions in 2007 and early 2008 by he Federal Reserve promoed liquidiy injecions. The resuls from my model sugges ha coinciden policy aimed a credi (i.e. capial requiremens, leverage raios, ec.) migh have decreased spreads much more by driving down risk premia. Comparing he linear equaions for spreads from my model o OLS regression resuls suggess ha he no-arbirage resricions imposed on he esimaion of he response coefficiens b n dampen he effec of he liquidiy facor relaive o he OLS resuls, while he resuls for he ineres rae and credi facors are similar across he wo specificaions. The predicive power of he model and he fac ha i allows exac idenificaion of ime-varying risk premia due o no-arbirage provides policymakers wih anoher ool when analyzing how moneary policy should reac o movemens in financial markes going forward. The seup of his paper is as follows. Secion 1 describes LIBOR and OIS conracs. Secion 2 oulines he model and moivaes he affine model used in his analysis as an alernaive o common inuiion underlying models of inerbank raes. Secion 3 deails he esimaion procedure and resuls. Secion 4 describes he behavior of LOIS spreads prediced by he model. Secion 5 discusses he imporance of risk premia. Secion 6 concludes. 5

6 1 LIBOR and Overnigh Index Swaps This secion provides deails on he LOIS ineres rae spreads by describing he LIBOR and OIS conracs and explaining heir behavior during he recen financial crisis. 1.1 LIBOR Ineres Raes LIBOR sands for he London Inerbank Offered Rae published by he Briish Banker s Associaion. LIBOR indicaes he average rae ha a paricipaing insiuion can obain unsecured funding for a given period of ime in a given currency in he London money marke. The raes are calculaed based on he rimmed, arihmeic mean of he middle wo quariles of rae submissions from a panel of he larges, mos acive banks in each currency. In he case of he U.S. LIBOR, he panel consiss of fifeen banks. These raes are a benchmark for a wide range of financial insrumens including fuures, swaps, variable rae morgages, and even currencies. Each paricipaing bank is asked o base is quoed rae on he following quesion: "A wha rae could you borrow funds, were you o do so by asking for and hen acceping inerbank offers in a reasonable marke size jus prior o 11 a.m. London ime?" An imporan disincion is ha his is an offered rae, no a bid rae, for a loan conrac. Acual ransacions may no occur a his offered rae, bu LIBOR raes do reflec he rue cos of borrowing given he sophisicaed mehods each paricipaing bank has a is disposal o ascerain risks in he underlying financial markes when i chooses o ener financial conracs. 1 1 Conroversy has been raised over he reliabiliy of he offering raes ha LIBOR banks were posing during he crisis. Insiuions were hough o be quoing lower raes a which hey could ake on inerbank loans in an effor o disguise any defaul risk hey hough was presen in heir respecive insiuion. However, his paper looks a spreads beween LIBOR and comparable ineres raes, and hus he spreads repored in his paper are consisen wih a lower bound on spreads ha migh have been repored if offered raes had been higher during he crisis. 6

7 Figure 2 plos he weekly averages of he daily Federal Funds rae along wih weekly averages of he daily one-, hree-, and welve-monh LIBOR raes. Before he onse of he 6 5 One Monh LIBOR Three Monh LIBOR Twelve Monh LIBOR Federal Funds Rae 4 Percen / / / / / /2009 Figure 2: Weekly averages of daily daa of he Federal Funds rae and he London Inerbank Offering Raes (LIBOR) a he one-, hree-, and welve-monh mauriies for he US Dollar. LIBOR is compued using a rimmed mean of he offering raes of fifeen paricipans banks. financial crisis, LIBOR raes closely racked he Federal Funds rae. Ye wih he crisis came a decoupling of LIBOR raes from he Federal Funds rae, wih LIBOR raes flucuaing above he Federal Funds rae. While comparing hese wo raes is ineresing, he Federal Funds rae is an overnigh rae, while LIBOR is a erm rae. Therefore, he nex secion will discuss an ineres rae wih comparable mauriy o he LIBOR rae ha capures movemens in he Federal Funds rae. 7

8 1.2 Overnigh Index Swaps An overnigh indexed swap (OIS) is a fixed/floaing ineres rae swap where he floaing rae is deermined by he geomeric average of a published overnigh index rae over each ime inerval of he conrac period. The wo counerparies of an OIS conrac agree o exchange, a mauriy, he difference beween ineres accrued a he agreed fixed rae and he floaing rae on he noional amoun of he conrac. The pary paying he fixed OIS rae is, in essence, borrowing cash from he lender ha receives he fixed OIS rae. No principal is exchanged a he beginning of he conrac. In conras o a plain vanilla swap, here are no inermediae ineres paymens. In he case of he Unied Saes, he floaing rae of he OIS conrac is ied o he Federal Funds rae. The fixed rae of an OIS in he Unied Saes is mean he capure he expeced Federal Funds rae over he erm of he swap plus any poenial risk premia. I is useful o undersand he mechanics of how an OIS operaes. Assume ha he ime inerval is weekly, where w reflecs he number of weeks in he conrac of he swap. Le N denoe he noional amoun of he OIS, i f ixed he fixed rae, i f loa he floaing rae, i FF, he Federal Funds rae a ime, and T he mauriy dae. Table 1 shows he paymens made during he duraion of he swap, where he floaing rae of he swap is compued using he formula below: i f loa = 52 w [ T 1 ( 1 + i ) ] FF,i 1. (2) i= 52 As a simple example, assume ha a one-monh OIS conrac is signed on = 01/01/2009 o maure a ime T = 02/01/2009. This implies ha here are four relevan Federal Funds raes ha will be used o compue he floaing rae given by equaion (2) a ime T. On 01/01/2009, wo paries agree o exchange N = $1000 a a fixed rae of i f ixed = 5.05%. Pary A is he receiving pary of he swap, which means hey receive he fixed rae i f ixed and pay 8

9 Time Floaing Rae Payer Fixed Rae Payer Ne Paymens T N i f loa w 52 N i f ixed w 52 N i f loa i f ixed w 52 Table 1: This able shows he paymens made by each paricipan in an OIS swap. N is he noional amoun of he swap, i f loa is he floaing paymen of he swap, i f ixed is he fixed paymen of he swap, w is he number of weeks in he swap, and T is he mauriy dae. he floaing rae i f loa. Pary B mainains he opposie posiion, receiving he floaing rae and paying he fixed rae. A ime T, when compuing he floaing rae, he following sream of Federal Funds raes are observed: i FF,1/1 = 5.00%, i FF,1/8 = 5.05%, i FF,1/15 = 5.01%, and i FF,1/22 = 5.01%. Given his informaion, he floaing rae is compued as: i f loa = 52 [( )( )( )( ) ] = 13 [( )( )( )( ) 1] = = 5.02%. Therefore, he ne paymen o Pary A (since he/she paid he lower ineres rae of i f loa = 5.02%) will be $ % 13 1 = $2.31. The ne paymen is much smaller han he noional amoun of he OIS. This reflecs ha he fixed rae was a good approximaion of he expeced Federal Funds rae over he erm of he conrac, and also ha he OIS conrac is no conaminaed wih as high a level of defaul or liquidiy characerisics as LIBOR. Figure 3 shows how OIS fixed raes have moved during he financial crisis, and compares hem o movemens in he underlying Federal Funds rae. The figure plos weekly averages of he daily Federal Funds rae and weekly averages of he daily one-, hree-, and welvemonh OIS raes based on an average of OIS raes quoed each day. Even wih he onse 9

10 of he crisis, OIS raes remained very close o he Federal Funds rae. Longer-erm OIS raes differ from shor-erm OIS raes due o he longer lengh of he conrac and more uncerainy in movemens of he underlying Federal Funds rae. 6 5 One Monh OIS Three Monh OIS Twelve Monh OIS Federal Funds Rae 4 Percen / / / / / /2009 Figure 3: Weekly averages of daily daa of OIS fixed raes a he one-, hree-, and welve-monh mauriies for he US Dollar. The index used for compued he floaing leg is he Federal Funds rae. 1.3 Moivaion for a Model of LOIS Spreads Suppose we specify a model for he erm srucure of unsecured, longer-erm inerbank ineres raes. Wih he yield curve derived from his model, we can price a variey of derivaives, including forward conracs and swaps. Le i (1) rae a ime, i (n) f (n 1) (n) denoe he shor-erm inerbank he longer-erm inerbank rae a ime ha maures a ime + n, and he forward rae a ime for a conrac ha sars in ime + n 1 and ends 10

11 a ime + n. The common way o derive forward raes is by using curren, shor-erm inerbank raes using he following formula: f (n 1) (n) = E [i (1) +n 1 ] + c. (3) Equaion (3) saes ha he forward rae is he expeced fuure shor rae E [i (1) +n 1 ] plus a consan erm premium c. Therefore, any movemens in he shor end of he inerbank yield curve will direcly impac forward raes. Ineres rae swaps on inerbank ineres raes are essenially bundles of forward conracs on he underlying shor-erm inerbank ineres rae. Therefore, he yield curve for inerbank raes will imply a series of forward raes, and bundling hese forward raes provides us wih swap raes. Figure 4 provides a diagram of an unsecured, longer-erm ineres rae i (n) (e.g. he LIBOR rae), and he inervals of shor-erm ineres raes beween he sar ime and he mauriy dae + T from which he swap rae (e.g he OIS rae) will be calculaed. Wih he enire yield curve for unsecured inerbank raes, swap raes can be compued using he shor-erm ineres rae from ha yield curve. Using Figure 4, we can back ou ha he longer-erm rae i (n) is approximaely equal o he probabiliy of defaul (ignoring liquidiy effecs) over he ime inerval [, T ], while he swap rae is he geomeric average of he probabiliy of defaul in he inervals [, + 1], [ + 1, + 2],...,[T 1,T ] generaed by rolling over each of he spo raes a each ime inerval. If i s he case ha longer-erm raes are high due o he probabiliy of defaul (i.e. defaul raes are higher over longer horizons), hen forward conracs on he shor-erm rae mus be high as well. This is because any defaul priced ino he unsecured, inerbank yield curve will be picked up by he shor rae i (1), and hus forward raes will reflec i, as well, as seen in equaion (3). Therefore, spreads beween unsecured, longer-erm inerbank raes 11

12 Figure 4: Comparison of LIBOR vs. OIS. like LIBOR and heir swap counerpars like OIS would be low, a predicion rejeced by he daa during he financial crisis. Why migh LOIS spreads be so high? Firs, he unsecured naure of LIBOR loans implies ha he quoed borrowing raes provided by LIBOR-paricipaing insiuions mus ake ino accoun he lack of collaeral posed a he sar of he conrac. A second reason is because he probabiliy of defaul (and/or liquidiy pressures) beween, for example [T 1, T ], is much higher han he probabiliy of defaul beween [, + 1], and he geomeric averaging performed in compuing swap raes creaes a large difference beween he probabiliy of defaul beween [, T ] and he average of he smaller ime inervals. Lasly, he paries involved in shor- vs. longer-erm conracs migh differ. High-defaul insiuions could show up for longer-erm loans, while low-defaul insiuions show up for shor-erm loans. 2 This implies ha he OIS is a derivaive ha has as he basis a shor-erm rae for low- 2 Indeed, while only 15 insiuions paricipae in he LIBOR survey, over 30 paricipae in he OIS marke. Therefore, he average probabiliy of defaul across all of he insiuions in he OIS marke could be far below ha for he LIBOR marke. 12

13 defaul insiuions, while he longer-erm LIBOR rae is high for high-defaul insiuions. Therefore, aking a geomeric average of he shor-erm rae when compuing he forward conracs ha make up he OIS rae provides a lower rae han he longer-erm LIBOR rae due o he defaul adjusmen. In he nex secion, I will provide a model ha reconciles spreads beween LIBOR and OIS raes using an adjused shor rae for LIBOR loans ha akes accoun of credi and liquidiy facors. 2 Model of he Term Srucure of Money Marke Spreads I describe a model of he LOIS erm srucure during he financial crisis ha incorporaes movemens in credi and liquidiy facors and relies on boh he defaulable bond work of Duffie and Singleon (1999) and he no-arbirage, discree ime affine models of Ang and Piazzesi (2003). LIBOR and OIS will each be modeled as zero-coupon bonds, and he assumpion of no-arbirage provides closed-form soluions for boh prices and yields of hese bonds. 2.1 VAR Dynamics As in Ang and Piazzesi (2003), suppose X is a 3-dimensional vecor of sae variables driving he economy, and assume ha X follows a Gaussian VAR(1) process: X = µ + ΦX 1 + Σε, (4) where ε iid N(0,I), Σ is assumed o be lower-riangular, and is a a weekly frequency. In his analysis, X consiss of (in order) an ineres rae facor r, a credi facor C, and a liquidiy facor L, all of which are observable variables. ε is he vecor of shocks driving he sysem in equaion (4), and he sysem is Cholesky facorized in order o separaely 13

14 idenify he impac of shocks o he sysem. 2.2 The LOIS Term Srucure Le i L,(n) denoe he n-period LIBOR rae, and i O,(n) following assumpions on he shor-erm ineres raes: he n-period OIS rae. I make he i O,(1) = r (5) i L,(1) = i O,(1) + γ. (6) The adjusmen erm γ is linear X : γ = γ 0 + γ T 1 X, (7) where γ1 T = (0,γ 1,1,γ 1,2 ) picks up movemens in he credi and liquidiy facors. Equaion (6) saes ha he shor-erm rae for LIBOR is equal o he shor-erm rae for OIS plus γ, which depends on he credi and liquidiy facors. Here, I assume ha he Federal Funds rae is he benchmark, safes shor-erm rae for he inerbank marke Marke Prices of Risk In order o derive he LOIS erm srucure under no-arbirage, I posi a paricular pricing kernel for he pricing of LIBOR and OIS securiies, which will be given by he following convenien form: m +1 = exp( shorrae )exp( 0.5λ T λ λ T ε +1 ), (8) 14

15 where he marke price of risk λ is linear in he sae vecor: λ = l 0 + l 1 X. (9) Taking logs and rewriing equaion (8) implies ha ln(m +1 ) = shorrae 0.5λ T λ λ T ε +1. (10) The log pricing kernel in equaion (10) is condiionally normally disribued, wih E [ln(m +1 )] = shorrae. Therefore, he pricing kernel (8) is condiionally log-normally disribued, wih E [m +1 ] = exp( shorrae ). A log-normally-disribued pricing kernel of a similar form can be derived from he uiliy maximizaion problem of a represenaive consumer wih CRRA uiliy and log-normally-disribued consumpion growh. To see his, recall ha he nominal pricing kernel for such a represenaive agen is given by he following formula: m +1 Π +1 = β ( C+1 C ) γ, where β is he discoun facor, C is consumpion a dae, γ is he coefficien of relaive risk aversion, and Π +1 is he gross rae of inflaion beween periods and + 1. Assuming ln ( C +1 ) C N(µc,,σc,) 2 and wih assumpions on he processes for µ c, and σc,, 2 we can obain pricing kernels similar o equaion (8). 3 The pricing kernel has wo componens. Firs, here is sandard discouning given by he erm exp( shorrae ), where shorrae will be given by equaion (5) for OIS raes and equaion (6) for LIBOR raes. Second, here is an added erm exp( 0.5λ T λ λ T ε +1 ) ha incorporaes he risk premia λ. This erm does no differ across LIBOR and OIS, which 3 For an overview of he consumpion-based pricing kernels, see Campbell, Lo, and MacKinlay (1997) and Cochrane (2005). 15

16 implies ha he uncerainy embedded wihin he pricing kernel does no differ across he wo securiies. In he absence of risk premia in which λ = 0, invesors are risk neural and he Expecaions Hypohesis would hold, implying ha longer-erm ineres raes equal he expecaions of fuure shor-erm raes no adjused for ime-varying risk. Risk premia in his model are linear, where l 0 capures he consan risk premia and l 1 capures any ime-variaion in risk premia The Difference Beween γ and λ Two key feaures of he model are equaion (7) for γ and equaion (9) for λ. Boh are linear funcions of he sae vecor X, bu heir roles in he model are disinc. γ is moivaed by he coninuous-ime models of Duffie and Singleon (1999), which specify affine, noarbirage models for unsecured, longer-erm zero-coupon bonds. The auhors show how affine assumpions on he defaul and/or liquidiy processes of hese asses imply closed form soluions for boh prices and yields. Assume ha, condiional on no defaul before ime, he probabiliy of defaul beween s and s + 1 for s > is given by c s. In addiion, assume ha he liquidiy of he asse beween s and s + 1 be given by l s. If he processes for c and l are specified as affine and exogenous, hen unsecured, longer-erm ineres raes can be derived using an adjused shor-erm ineres rae, an implici rae composed of he rue shor-erm ineres rae and adjusmens for he defaul and liquidiy processes. 4 he model, he wedge beween he LIBOR shor rae i L,(1) i O,(1) In and he rue inerbank shor rae = r is γ, which is affine in X and deerminisic. Any difference beween he LIBOR shor rae and he rue inerbank shor rae is due o a consan plus movemens in he credi and liquidiy facors. 4 The coninuous-ime-o-discree-ime conversion relies on several echnical condiions oulined in Duffie and Singleon (1999). 16

17 λ represens he risk premia in he model. In order o make asses aracive o risk averse invesors, he asses are priced wih a premia given by λ ha is aached o unexpeced movemens in he sae vecor X. In his model, λ is a hree-dimensional vecor ha measures ineres rae, credi, and liquidiy risks. Alhough λ is known a ime, is effec on pricing is no realized unil ime + 1. This can be seen hrough he pricing kernel equaion (8) where λ is aached o ε +1, he shocks o he sae vecor X +1. If λ = 0, hen he pricing kernel would collapse o exp( shorrae ) and all pricing would be done as if invesors were risk neural. Noe, however, ha he shor rae erm sill depends on γ. γ can be non-zero for boh risk averse and risk neural invesors, whereas λ can be nonzero only for risk averse invesors No-Arbirage Pricing Funcions For a zero-coupon bond a ime wih mauriy n and price P (n), he assumpion of noarbirage is equivalen o he following: P (n) = E [m +1 P (n 1) +1 ], (11) where P (1) = E [m +1 1] = exp( shorrae ). Applying his o he pricing funcions for boh LIBOR and OIS implies ha: P L,(n) = E [exp( i L,(1) )exp( 0.5λ T λ λ T ε +1 )P L,(n 1) +1 ] (12) P O,(n) = E [exp( i O,(1) )exp( 0.5λ T λ λ T ε +1 )P O,(n 1) +1 ], (13) where P L,(n) is he price of he n-period LIBOR and P O,(n) is he price of he n-period OIS. I subsiue for he pricing kernel given by equaion (8) wih he appropriae shor rae for each securiy. I conjecure ha he pricing funcions are exponenial affine in he sae 17

18 vecor: P L,(n) = exp(a L,n + B T L,nX ) (14) P O,(n) = exp(a O,n + B T O,n X ). (15) Using he conjecure on LIBOR given by equaion (14) and he assumpions on he shor raes given by equaions (5) and (6) leads o he following soluion for he recursive LIBOR coefficiens: A L,n+1 = A L,n + B T L,n(µ Σl 0 ) + 0.5B T L,nΣΣ T B L,n γ 0 (16) B T L,n+1 = B T L,n(Φ Σl 1 ) (1,γ 1,1,γ 1,2 ), (17) where A L,1 = γ 0 and B T L,1 = (1,γ 1,1,γ 1,2 ) T. Using a similar conjecure on OIS, he recursive coefficiens for OIS are given by: A O,n+1 = A O,n + B T O,n (µ Σl 0) + 0.5B T O,n ΣΣT B O,n (18) B T O,n+1 = B T O,n (Φ Σl 1) (1,0,0), (19) where A O,1 = 0 and B T O,1 = (1,0,0)T. Using hese recursive coefficiens, he coninuously-compounded yields for LIBOR and OIS can be wrien as: i L,(n) = a L,n + b T L,nX (20) i O,(n) = a O,n + b T O,n X, (21) where a L,n = A L,n /n and a O,n = A O,n /n are he consans, and b T L,n = BT L,n /n and 18

19 b T O,n = BT O,n /n are he response coefficiens for he LIBOR and OIS yields, respecively. 2.3 LOIS Spreads Given he closed form soluions (20) and (21), define he LOIS spread for mauriy n as: z (n) = i L,(n) i O,(n) = (a L,n + b T L,nX ) (a O,n + b T O,n X ) = a n + b T nx, (22) where a n a L,n a O,n and b T n b T L,n bt O,n. Wha is of ineres in he analysis in his paper is he response coefficien vecor b n, since i deermines how spreads respond o movemens in he underlying facors of he economy. While he model is linear, hese coefficiens b n have risk premia buil ino hem, and I will examine how behavior of his risk premia generaes movemens in spreads. 3 Daa and Economeric Mehodology This secion describes he daa and esimaion procedure used for he model specified in Secion 2, as well as any robusness exercises. 3.1 Daa The sample period used for esimaion is from 1/1/2007-6/18/2009, which encompasses he lead-up o and duraion of he financial crisis. For he esimaion, I use weekly averages of daily daa for one-, hree-, six-, nine-, and welve-monh mauriies of LIBOR i L,(n) OIS raes i O,(n). I use hese o compue he LOIS spreads z (n) o be used in he esimaion, and 19

20 which are ploed in Figure 1. In order o esimae he shor rae parameers γ 0 and γ 1, I use daa on he one-week LIBOR rae. For robusness, raher han using LIBOR raes as a measure of unsecured, longer-erm inerbank borrowing, I esimae he model using erm Federal Funds raes. These are raes on longer-erm inerbank borrowing in he Federal Funds marke, as opposed o he LIBOR marke. Any issues abou how he LIBOR survey is conduced and how his would bias he LIBOR raes repored by he BBA is no presen in hese erm Federal Funds raes. Esimaion resuls for he erm Federal Funds raes in place of LIBOR is repored in he appendix in Table 12. The vecor of economic facors X includes weekly averages of daily daa on he Federal Funds rae r, he credi facor C, and he liquidiy facor L. In Figure 5, I plo he Federal Funds rae, along wih he credi and liquidiy facors described below The Credi Facor For he credi facor, I use he spread beween he hree-monh LIBOR and he hree-monh inerbank repurchase agreemen raes. Repurchase agreemens (REPOs) are secured financial conracs ha allow he borrower o use financial securiies as collaeral for cash loans a a fixed ineres rae, in conras o LIBOR conracs which are unsecured. Here, I have used REPOs in which essenially defaul-free U.S. Treasury securiies are posed as collaeral, which allows me o idenify hese inerbank REPOs as safe, collaeralized inerbank loans. Therefore, he spread beween LIBOR and REPO raes is a measure of he credi in he inerbank marke. In addiion, since paries involved in LIBOR and REPO conracs are similar, any variaion in liquidiy would be common across he wo securiies and removed once examining he spread. In addiion, I perform robusness exercises using oher measures of he credi facor, including: (1) he one-monh LIBOR-REPO spread, (2) he median five-year credi defaul swap 20

21 6 5 Federal Funds Rae Credi Facor Liquidiy Facor 4 Percen / / / / / /2009 Figure 5: Weekly averages of daily daa on he ineres rae, credi, and liquidiy facors. The ineres rae facor is he Federal Funds rae, he credi facor is he hree-monh LIBOR-REPO spread, and he liquidiy facor is he on/off-he-run en-year U.S. Treasury premium. (CDS) rae for LIBOR insiuions, (3) he mean of all hree of he credi measures, and (4) he firs principal componen of all hree of hese measures. The resuls of he robusness across differen measures of his credi facor are repored in he appendix in Tables 11 and 12. CDS are essenially insurance policies on corporae bonds. The buyer of a CDS pays a periodic fee o he seller in exchange for a promise of paymen, in he even of bankrupcy or defaul of he insiuion ha issued he bond, equal o he difference beween he par and marke values of he bond. The CDS raes in he daa are repored in erms of he premium o be paid. For example, suppose he five-year CDS for Big Bank Corp. was 21

22 quoed around 160 bps on January 1, This means ha if you wan o buy he 5-year proecion for a $100 million exposure o Big Bank Corp. credi, you would pay 40 bps, or $400,000, every quarer as an insurance premium in he even of defaul. Figure 6 plos he one-monh LIBOR-REPO spread, hree-monh LIBOR-REPO spread, and five-year CDS median over he sample period. The firs wo measures follow each oher closely, while he CDS median has mainained an upward rend hroughou he sample period One Monh LIBOR REPO Three Monh LIBOR REPO Five Year CDS Median Percen / / / / / /2009 Figure 6: Weekly averages of daily daa on he one-monh LIBOR-REPO spread, hree-monh LIBOR-REPO spread, and he median five-year CDS rae for LIBOR paricipans insiuions The Liquidiy Facor For he liquidiy facor, I use he premium beween on-he-run and off-he-run en-year U.S. Treasury securiies. The on/off-he-run premium resuls from he fac ha off-he-run secu- 22

23 riies are sold a a discoun o comparable on-he-run securiies. On-he-run securiies are more liquid relaive o off-he-run securiies due o search echnologies in hese markes, heir large volume a issuance, sophisicaion of he paricipaing invesors, relaive supply of each in he secondary marke, ec., as sressed in papers such as Duffie e.al. (2005), Vayanos and Weill (2008), and Pasquariello and Vega (2009). The on-he-run daa series is he yield of he curren en-year on-he-run securiy as provided by he Federal Reserve Bank of New York, while he off-he-run daa series is a synheic series of he off-he-run equivalen yield of he curren en-year on-he-run securiy using a zero-coupon yield curve. Longsaff (2004) discusses a similar measure using he difference beween Treasury bond prices and he prices of bonds issued by he Resoluion Funding Corporaion (Refcorp), which is fully-collaeralized by he U.S. governmen. Schwarz (2009) uses a measure of liquidiy similar o Longsaff (2004), paricularly he difference beween German governmen bonds and bonds issued by he KfW developmen bank, boh of which are backed by he German governmen. Empirical invesigaions of liquidiy in he U.S. Treasury marke have been examined by various auhors. Brand and Kavajecz (2003) examine price discovery hroughou he relaionship beween liquidiy, order flow, and he yield curve. Fleming (2003) documens he ime series behavior of a se of liquidiy measures, including he on/off-he-run premium, using high-frequency daa and poins ou he advanages and disadvanages of cerain measures over ohers. Finally, Chordia e.al.(2005) examines liquidiy across equiy and fixedincome markes and shows using vecor auoregressions ha liquidiy wihin and across hese wo markes is highly correlaed, implying ha a common facor drives liquidiy in hese markes. The measure of liquidiy I use is mean o capure marke liquidiy, he ease a which an asse can be raded. Brunnermeier and Pederson (2009) provide a model ha sresses he 23

24 difference beween an asse s marke liquidiy and a rader s funding liquidiy, or he ease a which raders can obain funding. Marke liquidiy is asse-specific, and is modeled as any deviaion of an asse s price from is fundamenal value. The on- and off-he-run securiies have idenical fuure cash flows, and hus hey should have he same fundamenal value. The on/off-he-run premium exiss because one (or boh) of he prices differs from he fundamenal value. Funding liquidiy is agen specific, bu he wo conceps are muually reinforcing. However, since marke liquidiy is asse-specific, issues can arise using a U.S. Treasury measure of liquidiy for an analysis sudying he LIBOR marke. While a LIBOR measure of liquidiy would be mos desirable, calculaing such a measure using radiional merics such as bid-ask spreads, marke frequency and volume, or price impac coefficiens leaves a liquidiy measure ha is conaminaed by he defaul characerisics of LIBOR. The on/off-he-run premium avoids his issue, since he underlying bonds are backed by he (essenially) defaul-free U.S. governmen. 3.2 Esimaion Procedure In order o esimae he model, define η,n as he vecor of residuals: η,n = z (n) ẑ (n) = z (n) â n ˆb T nx = z (n) (â L,n â O,n ) (ˆb T L,n ˆb T O,n )X, (23) where z (n) denoes he acual LOIS spreads and ẑ (n) = â n ˆb T n X are prediced LOIS spreads from he heoreical model. Using hese errors η, he esimaion procedure involves wo sages: 24

25 (i) Fix µ o mach he uncondiional mean of X. Using seemingly unrelaed regressions (i.e. OLS equaion-by-equaion), esimae Θ 1 (Φ,Σ,γ 0,γ 1 ). (ii) Holding Θ 1 fixed, esimae Θ 2 (l 0,l 1 ) using non-linear leas squares, where he minimizaion problem is given by: min l 0,l 1 T N =1 n=1 η (2). (24) Since he objecive funcion is highly non-linear, I esimae he model 10,000 imes in order o ge reliable saring values for he minimizaion procedure. I hen esimae he model around hese saring values o find he minimum. I compue firs-sage robus GMM sandard errors. To correc for any firs-sage esimaion error, second sage sandard errors are compued by boosrapping he daa sample 10,000 imes and aking he poserior sandard deviaion of he parameer esimaes. 3.3 Parameer Esimaes Table 2 repors esimaion resuls for Θ 1, which includes he VAR dynamics and he shor rae equaion for i L,(1). The firs row of he marix Φ corresponds o he equaion for he Federal Funds rae r, he second row corresponds o he equaion for he credi facor C, and he hird row corresponds o he equaion for he liquidiy facor L. The firs column of Φ corresponds o he parameer esimae for he impac of r 1 on each of he variables in X, while he second and hird columns correspond o he effecs of C 1 and L 1 on he variables in X, respecively. C 1 is esimaed o be saisically significan in each of he equaions of he VAR, while r 1 and L 1 are significan only in he equaions corresponding o hemselves. This implies ha he credi facor Granger-causes he oher facors, hus having significan predicive power for movemens in boh he Federal Funds 25

26 rae and he liquidiy facor. Innovaions o each of he facors exhibi low correlaion as repored by he esimaed off-diagonal elemens of ΣΣ T. This implies ha he Cholesky idenificaion of shocks is saisfied and does no resric he parameer esimaes. 5 VAR Dynamics Shor Rae Dynamics X Φ ΣΣ T γ 0 γ 1 r (0.02) (0.03) (0.15) (0.05) C (0.04) (0.07) (0.48) (0.14) L (0.00) (0.01) (0.04) (0.29) Table 2: This able repors he esimaed coefficiens of he VAR and shor rae equaions in Θ 1. The full sample of daa is 01/01/ /19/2009. The esimaed VAR is X = Φ X 1 + Σε. X consiss of he Federal Funds rae r, he credi facor C, and he liquidiy facor L. X is X E[X ] in an effor o pin down he uncondiional mean of he vecor X. Σ is Cholesky-facorized, and ε N(0,I). The shor rae coefficiens are esimaed according o i (1) = γ 0 + γ 1 X, where i (1) is he one-week LIBOR rae, and γ 1 is consrained as γ 1 = (1,γ 1,1,γ 1,2 ). Esimaion is performed using ordinary leas squares. Robus GMM sandard errors are repored below coefficien esimaes. The shor rae dynamics for he esimaion î L,(1) can be found on he righ side of Table 2. The firs elemen of γ 1 corresponds o he Federal Funds rae (which is idenical o he shorerm OIS rae i O,(1) ), and is consrained o be one as given by equaions (5) and (6). From he esimaes, a one percen increase in he credi facor increases he shor-erm LIBOR rae by 0.8%, while a one percen increase in he liquidiy facor acually decreases he shor-erm LIBOR rae by 0.95%. Condiional on movemens in credi, liquidiy imposes a negaive premium on he shor-erm rae. This could be due o a larger amoun of longererm invesors in he marke, or due o expecaions of falling shor-erm ineres raes in 5 Esimaing an AR(1) process for he Federal Funds rae r shows ha here is a uni roo in he process for r. However, he VAR(1) specificaion allows me o pin down he saionary dynamics of he Federal Funds rae, since i no only depends on is own lags bu lags of boh he credi facor C and he liquidiy facor L. The eigenvalues of he sysem are all wihin he uni circle, wih he modulus of he eigenvalue vecor given by (0.99, 0.91, 0.91). 26

27 he fuure. 6 Figure 7 plos he wo shor-erm raes and he esimaed ˆγ premium. The solid black line is he shor-erm OIS rae i O,(1) î L,(1), and he dashed line is he esimae of ˆγ = î L,(1) = r, he green line is he esimaed shor-erm LIBOR rae i O,(1). In he early par of he sample before he crisis, he ˆγ premium was zero, and began increasing in he summer of During he panic in lae 2008, he premium increased o over 2%, and has seled back down o near zero since. Even hough he liquidiy facor was esimaed wih a negaive coefficien in he equaion for ˆγ, he esimaed effec of he credi facor is far larger han ha for he liquidiy facor and resuls in a posiive ˆγ. Turning o he dynamic responses of each of he facors o shocks o he VAR, Figure 8 plos he impulse response funcions (IRF) from he VAR. Each panel depics he Choleskydecomposed response of a one-sandard deviaion shock o he relevan facor. The firs row of Figure 8 shows how each of he facors responds o shocks o he Federal Funds rae r. Ineresingly, a posiive shock o r has a negaive impac on he credi facor C. Common inuiion would associae effecive loosening of policy (i.e. a decrease in r ) wih a similar decrease in he credi facor, ye he sandard policy of lowering he Federal Funds rae during his crisis did no lower he credi facor. Pressures due o credi remained in markes even hough he Federal Reserve plummeed he Federal Funds rae down o zero. However, he liquidiy facor L showed no significan reacion o a shock o r. Turning o he second row of Figure 8, we can examine he impac of shocks o C. Neiher r nor L exhibi significan reacions o shocks o C. Lasly, row hree shows ha shocks o L have a posiive impac on C. This means ha as here is less liquidiy in he markes (i.e. an increase in L ), here is a higher amoun of credi pressures, as well. Table 3 repors he 6 In he robusness exercises repored in he appendix, boh he one-monh LIBOR-REPO spread and CDS median credi facors do no exhibi his negaive coefficien on he liquidiy facor in he equaion for γ. 27

28 6 5 i O,(1) i L,(1) γ 4 Percen / / / / / /2009 Figure 7: Comparison of LIBOR and OIS shor raes from (5) and (6) and he γ premium. The full sample of daa is 01/01/ /19/2009. γ is esimaed by regressing he one-week LIBOR rae minus he Federal Funds rae on a consan, he credi facor C, and he liquidiy facor L. The parameers are repored in Table 2. The solid black line is he shor-erm OIS rae i O,(1) = r, he green line is he esimaed shor-erm LIBOR rae î L,(1) ˆγ = î L,(1) i O,(1)., and he dashed line is he esimae of variance decomposiion of each of he facors from he VAR. Each panel represens how much of he forecas error variance of a paricular facor is due o each of he facors in X as he forecas horizon increases. Panel A decomposes how much of he forecas error variance of r is due o each of he facors. A he four-week horizon, mos of he variaion is due o r iself. However, as he horizon increases, C begins o explain more of he variaion. 41% of he uncondiional forecas error variance (i.e. h = ) of r is due o C, while only 14% is due o L. 28

29 Federal Funds Rae Shock o Federal Funds Rae Federal Funds Rae Shock o Credi Facor Federal Funds Rae Shock o Liquidiy Facor Credi Facor Shock o Federal Funds Rae 0.3 Credi Facor Shock o Credi Facor 0.05 Credi Facor Shock o Liquidiy Facor Liquidiy Facor Shock o Federal Funds Rae Liquidiy Facor Shock o Credi Facor 0.04 Liquidiy Facor Shock o Liquidiy Facor Figure 8: Impulse response funcions of he VAR X = µ + ΦX 1 + Σε. X consiss of he ineres rae facor r, he credi facor C, and he liquidiy facor L. Σ is Cholesky-facorized, and ε N(0,I). Each figure plos he IRF of each of he facors o one sandard deviaion responses in a paricular facor. Sandard error bands are repored around esimaed IRFs. Turning o Panel B, he majoriy of he variaion in C is due o iself, wih only a small decrease in he proporion of he variance explained by iself as he horizon increases. Lasly, Panel C shows how he forecas error variaion of L is decomposed. A he shores horizon, L explains he larges proporion. However, by he welve-week horizon, C begin o explain he majoriy proporion, wih a maximum of 68% of he variaion a he wenyfour week horizon. The resuls of he variance decomposiion again highligh he predicive 29

30 power of he credi facor for no only iself, bu also boh he Federal Funds rae and liquidiy facor. Horizon h Percen aribued o (weeks) r C L Panel A: Federal Funds Rae Panel B: Credi Facor Panel C: Liquidiy Facor Table 3: The able repors uncondiional forecas error variance decomposiions (in percenages) for each of he variables in X. The forecas horizon h is in weeks. The full sample of daa is 01/01/ /19/2009. The esimaed VAR is X = µ + ΦX 1 + Σε. X consiss of he Federal Funds rae r, he credi facor C, and he liquidiy facor L. Σ is Cholesky-facorized, and ε N(0,I). Esimaion is performed using ordinary leas squares. Finally, Table 4 repors esimaes of he marke price of risk parameers Θ 2 from he second sage esimaion. The firs row of he able corresponds o r, he second row corresponds o C, and he hird row corresponds o L. The firs column repors he consan risk premia parameers l 0. Each facor has significanly-priced consan risk premia. Turning o l 1, we can idenify if here is any ime-varying risk premia associaed wih he facors. Indeed, all bu hree of he coefficiens are significanly differen from zero, implying here is also 30

31 significan ime-variaion in risk premia associaed wih all of he facors. Thus, he financial crisis proves o be a ime period useful for esimaing risk premia, and here is srong evidence for risk aversion (i.e. λ 0) during he crisis. l 0 l (0.02) (0.14) (0.11) (0.10) (0.09) (0.17) (0.34) (0.19) (0.04) (0.16) (0.14) (0.08) Table 4: This able repors esimaes of he marke price of risk parameers.the full sample of daa is 01/01/ /19/2009. The marke prices of risk are given by λ = l 0 + l 1 X, where X consiss of he ineres rae facor r, he credi facor C, and he liquidiy facor L. Esimaion is performed using non-linear leas squares. Boosrapped sandard errors are repored below coefficien esimaes. 3.4 Maching Momens Table 5 repors he means, sandard deviaions, and firs-order auocorrelaions of he LOIS spreads from boh he daa and prediced by he model. The model capures he uncondiional momens of LOIS spreads very well, including he sharp spike in volailiy winessed during he crisis, and only slighly underesimaes he auocorrelaion exhibied by LOIS spreads. All hree momens are (weakly) increasing funcions of mauriy of he LOIS spread, and he model is able o capure his general rend well. 4 The Dynamics of LOIS Spreads This secion will discuss he behavior of LOIS spreads generaed by he model by analyzing he response coefficiens from he linear equaion for spreads (22) and he dynamic response of spreads o each of facors in X. 31

32 PANEL A: MOMENTS OF SPREADS IN DATA Mean Sandard Deviaion Auocorrelaion One-Monh LOIS Three-Monh LOIS Six-Monh LOIS Nine-Monh LOIS Twelve-Monh LOIS PANEL B: MOMENTS OF SPREADS FROM MODEL Mean Sandard Deviaion Auocorrelaion One-Monh LOIS Three-Monh LOIS Six-Monh LOIS Nine-Monh LOIS Twelve-Monh LOIS Table 5: This ables repors he uncondiional momens of he LOIS spreads z (n) from he daa and prediced from he model. The full sample of daa is 01/01/ /19/2009. The momens include he mean, sandard deviaion, and firs-order auocorrelaion. Panel A repored he momens of spreads from he daa, and Panel B repors he model-prediced momens of spreads. 4.1 The Response Coefficiens Figure 9 plos he esimaed response coefficiens from equaion (22). For each mauriy, he response coefficien corresponds o how much he LOIS spread responds o a one percen increase in each of he facors. The dark solid line plos he esimaed coefficiens for r, he ligh solid line corresponds o he coefficiens for C, and he dashed line corresponds o he coefficiens for L. r has a negligible, negaive impac on he erm srucure of LOIS spreads, reflecing he fac ha he LOIS spread has removed general movemens in shorerm inerbank ineres raes capured by r. C has a posiive impac on LOIS spreads ha declines slighly wih mauriy. A he one-monh mauriy, a one percen increase in C implies an approximaely 0.8% increase in he LOIS spread. This effec decreases o a 0.48% increase in he LOIS spread a he welve-monh mauriy. 32

33 Percen Federal Funds Rae Credi Facor Liquidiy Facor Mauriy (weeks) Figure 9: Esimaed response coefficiens b n from he linear equaions for LOIS spreads given by z (n) = a n + b T n X as a funcion of he mauriy of he LOIS spread. The solid line shows how spreads reac o he Federal Funds rae, he dashed line shows he reacion o he credi facor, and he doed line shows he reacion o he liquidiy facor. L has an iniially negaive impac on LOIS spreads ha quickly increases o a posiive impac as he mauriy increases. The negaive response coefficien a he shorer-erm LOIS mauriies is relaed o he negaive coefficien esimaed on L in he equaion for γ ; condiional on credi, here is a negaive correlaion beween he shor end of he LOIS yield curve and liquidiy. However, as he mauriy of he LOIS spread increases, L has a posiive impac on LOIS spreads. A he welve-monh mauriy, a one percen increase in he liquidiy facor has an almos 1% increase in he LOIS spread. This reflecs he imporance of liquidiy as mauriy increases; longer-erm asses generae a larger liquidiy premium. 33

34 Figure 9 also repors OLS coefficiens and sandard error bands from he following regression: z (n) = α n + β 1,n r + β 2,n C + β 3,n L + ν. (25) The poin esimaes from he OLS esimaion are repored as symbols in he figure. Small dos correspond o he esimaes of β 1,n, small sars correspond o esimaes of β 2,n, and small crosses correspond o esimaes of β 3,n. The small dos are on op of he dark solid line, reflecing he fac ha he response coefficiens for r esimaed by he model are almos idenical he OLS poin esimaes from equaion (25). The sandard error bands around hese esimaes are also igh, and he response coefficien curve from he model lies wihin he sandard error band. The model also does well of maching he response coefficiens on C o hose prediced from he OLS regressions. In conras, he model does no mach he response coefficiens on L esimaed by OLS. The model predics ha he response coefficiens on L are lower han he OLS poin esimaes for all mauriies, even more so for he shorer mauriies. In addiion, he sandard error bands are much wider for he liquidiy facor. A he one-monh mauriy, he OLS coefficien is insignificanly differen from zero, implying ha liquidiy has almos no effec on he shores end of he LOIS yield curve. However, he response coefficien curve from he model lies almos enirely wihin he OLS sandard error bands, so he model-prediced response coefficiens are no saisically significanly differen from he OLS poin esimaes. The coefficiens from his OLS esimaion are relaed o hose repored in Taylor and Williams (2008), McAndrews e.al. (2008), and Schwarz (2009), which all use OLS regressions o ascerain he impac of credi and liquidiy on LOIS spreads. The linear relaionship beween LOIS spreads and he facors X prediced by he model implies ha he 34