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

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1 Finance and Economics Discussion Series Divisions of Research & Saisics and Moneary Affairs Federal Reserve Board, Washingon, D.C. Volailiy, Money Marke Raes, and he Transmission of Moneary Policy Seh B. Carpener and Selva Demiralp NOTE: Saff working papers in he Finance and Economics Discussion Series (FEDS) are preliminary maerials circulaed o simulae discussion and criical commen. The analysis and conclusions se forh are hose of he auhors and do no indicae concurrence by oher members of he research saff or he Board of Governors. References in publicaions o he Finance and Economics Discussion Series (oher han acknowledgemen) should be cleared wih he auhor(s) o proec he enaive characer of hese papers.

2 Volailiy, Money Marke Raes, and he Transmission of Moneary Policy Seh B. Carpener Senior Associae Direcor Division of Moneary Affairs Board of Governors of he Federal Reserve Sysem 20 h and C Sree, NW, Washingon, DC scarpener@frb.gov and Selva Demiralp Associae Professor Deparmen of Economics Koc Universiy Rumeli Feneri Yolu Sariyer, Isanbul Turkey sdemiralp@ku.edu.r February 2011 Absrac Cenral banks ypically conrol an overnigh ineres rae as heir policy ool, and he ransmission of moneary policy happens hrough he relaionship of his overnigh rae o he res of he yield curve. The expecaions hypohesis, ha longer-erm raes should equal expeced fuure shor-erm raes plus a erm premium, provides he ypical framework for undersanding his relaionship. We explore he effec of volailiy in he federal funds marke on he expecaions hypohesis in money markes. We presen wo major resuls. Firs, he expecaions hypohesis is likely o be rejeced in money markes if he realized federal funds rae is sudied insead of an appropriae measure of he expeced federal funds rae. Second, we find ha lower volailiy in he bank funding markes marke, all else equal, leads o a lower erm premium and hus longer-erm raes for a given seing of he overnigh rae. The resuls appear o hold for he US as well as he Euro Area and he UK. The resuls have implicaions for he design of operaional frameworks for he implemenaion of moneary policy and for he inerpreaion of he changes in he Libor-OIS spread during he financial crisis. We also demonsrae ha he expecaions hypohesis is more likely o hold he more closely linked he shor- and long-erm ineres raes are. Keywords: Moneary ransmission mechanism, expecaions hypohesis, erm premium JEL codes: E43, E52, E58 The views expressed are hose of he auhors and do no necessarily reflec hose of he Federal Reserve, he Board of Governors, or oher members of he saff. Demiralp s research was funded by he Turkish Academy of Sciences (TUBA). David Lucca,Ruslan Bikbov, Rehim Kilic, Benoi Mojon and he paricipans a he ECB s workshop on "Challenges o moneary policy implemenaion beyond he financial marke urbulence" provided useful discussions. We hank Zenide Avellaneda and Peer Andersen for excellen research assisance.

3 Inroducion Cenral banks ypically conrol an overnigh ineres rae as heir policy ool, and mos economiss hink ha he ransmission of moneary policy happens hrough he relaionship of his overnigh rae o he res of he yield curve. The expecaions hypohesis, ha longererm raes should equal expeced fuure shor-erm raes plus a erm premium, provides he ypical framework for undersanding his relaionship. The degree of conrol ha he Federal Reserve has exercised over he funds rae has no been consan hrough ime, and he recen financial crisis led o dislocaions in many money markes. We explore he effec ha volailiy in he federal funds marke has on he expecaions hypohesis in money markes. Specifically, we look for evidence ha volailiy in he overnigh rae can affec he erm premium embedded in longer-erm money marke raes. The Federal Reserve has had a arge for he federal funds rae for decades. Alhough from 1979 o 1982, he pah of nonborrowed reserves was he official operaing framework, boh before and afer, he Federal Open Marke Commiee had an inended level for he funds rae (see Bernanke and Blinder, 1992, Rudebusch, 1995, Meulendyke, 1998). The volailiy in he funds marke, however, has no been consan (see Benne and Perisiani, 2002, Hilon, 2005, Demiralp and Farley, 2005, Nauz and Schmid, 2009). Demiralp and Farley have documened he decline in volailiy in he funds marke during he 1990s, for example, and aribue he rend o higher frequency of open marke operaions on he par of he Federal Reserve, improved reserve managemen of banks, and consolidaions in he banking sysem. Nauz and Schmid (2009) noe ha he seps aken owards ransparency since 1994 furher sabilized he funds rae volailiy. As moneary policy in he Unied Saes has become more ransparen and predicable, he anicipaion of changes o he arge rae led o movemens in he funds rae before many arge rae changes. Carpener and Demiralp (2006) invesigae his phenomenon and documen ha here is some evidence ha 1

4 he anicipaion effec is ransmied o he very near end of he yield curve. In his paper, we ry o esimae wha effec more generalized volailiy in he federal funds rae has on longererm money marke raes. The expecaions hypohesis has been sudied exensively in he economics lieraure. Among he more noable examples are Shiller, Campbell, and Schoenholz, 1983, Campbell and Schiller, 1991, Mankiw and Miron, 1986, and Rudebusch, The lieraure provides mixed suppor for he expecaions hypohesis in is mos simple form, however, wih he allowance for (poenially ime-varying) erm premiums, he record improves. For he shor end of he yield curve, Lange, Sack, and Whiesell (2003), as an example, provide evidence ha he link beween expeced fuure shor raes and longer-erm raes has become sronger wih more ransparen and predicable moneary policy. Many researchers who have esed he expecaions hypohesis, however, have found very weak evidence a he shor end of he yield curve. Mankiw and Miron (1986) aribued he negligible predicive power of he spread beween long raes and shor raes o he Federal Reserve s ineres smoohing policies. They argued ha he Federal Reserve s ineres sabilizaion policies induced a random walk behavior a he shor end of he yield curve. Under hese circumsances and assuming raional expecaions, he shor rae expeced by he marke would always equal he curren shor rae, and he erm spread would always equal he erm premium. Flucuaions in he spread would have no predicive power for he pah of he shor rae. Mankiw and Miron s argumen is ha he Fed s ineres rae smoohing weakens he erm srucure relaionship by prevening any informaion abou he near-erm expecaions o be refleced in shor erm raes. In his paper, we noe ha he performance of he expecaions hypohesis a he shor end of he yield curve improves when an appropriae measure of he expeced federal funds rae is used. 2

5 Using daa from 1992 hrough 2010, we find ha lower volailiy in he funds marke leads, all else equal, o a lower erm premium and hus lower longer-erm raes for a given seing of he overnigh rae. The resul is fairly inuiive. One reason for he expecaions hypohesis o hold is hrough arbirage. If he erm rae was expeced o be above he expeced overnigh rae, a bank could borrow a he overnigh rae o fund a erm loan and earn he spread. Volailiy in he overnigh rae, however, creaes uncerainy in funding coss. If his uncerainy leads poenial arbirageurs o demand a risk premium for funding a erm loan hrough overnigh funds, he erm premium should rise. These resuls bear on he design of he framework for he implemenaion of moneary policy wih regard o he desirable degree of conrol over he overnigh rae. For example, while a simple framework may be desirable from an operaional perspecive, if a simple framework were o lead o an overnigh rae ha is volaile, erm premiums, and herefore longer-erm raes, would likely be higher. The resuls also sugges a differen, or perhaps addiional, inerpreaion of he changes in he Libor-OIS spread during he financial crisis. Researchers who sudied he crisis have looked for a link beween he Libor-OIS spread and counerpary risk, ofen measure by credi-defaul-swap (CDS) spreads (see for example, Taylor and Williams, 2009, McAndrews e al., 2009). Addiionally, researches have aribued narrowing in he spread o he Federal Reserve s liquidiy provision hrough various faciliies (see McAndrews e al., 2009, Chrisensen e al., 2009). Our resuls sugges an alernaive, bu easily complemenary, channel for he narrowing of he spread. Figure 1 plos he hree-monh Libor-OIS spread ogeher wih average inraday volailiy over he previous 30 days, along wih he median CDS spread for he banks in he Libor panel from January 2007 o Sepember Noe ha volailiy in he federal funds rae fell following he auumn of 2008, and he Libor-OIS spread declined seadily over he firs half of Inraday volailiy is a volume-weighed measure of sandard deviaion based on oal brokered funds rae ransacions on a given day. 3

6 The decline in volailiy could have led o a leas some of he narrowing of he Libor-OIS spread in addiion o any conribuion from reduced credi risk or cenral bank inervenions. The res of he paper is laid ou as follows. The nex secion discusses esimaion sraegies for he expecaions hypohesis, following he exising lieraure. We look a he effec of including differen measures of expecaions in he funds marke ino a sandard empirical specificaion and show ha he expecaions measures ha we use maers. The following secion shifs he focus o erm bank funding raes. We demonsrae ha he expecaions hypohesis appears o work well for bank funding raes and ha volailiy in he overnigh rae can conribue significanly o explaining erm premiums. This main resul is esablished for he US as well as he Euro Area and he UK. This resul is of paricular ineres in undersanding he erm premium during he financial crisis and in undersanding he implicaions of differen operaing environmens for he implemenaion of moneary policy. The final secion concludes. The Expecaions Hypohesis The expecaions hypohesis of he erm srucure of ineres raes saes ha curren longer-erm raes should equal o he average of he expeced overnigh rae plus some erm premium ha accouns for liquidiy risk, credi risk, or oher facors. In pracice, we could hink of he hree-monh Treasury bill rae (TB3) as he long-erm rae and he overnigh federal funds rae (FFR) o be he shor-erm rae. We could wrie he expecaions hypohesis as follows: TB 1 90 FFR E ( FFR ) E ( FFR )... E ( FFR c ) (1) Where E denoes he expecaions operaor a ime and c is a erm premium. In many empirical analysis of he erm srucure such as Campbell and Schiller, 1991, Mankiw and Miron, 1986, Roberds e al., 1996, and Lange e al., 2003, a common pracice is o assume 4

7 perfec foresigh such ha E ( FFR ) FFR and es wheher oday s 90-day Treasury i i rae is equal o he average realized (no expeced) funds raes over he nex 90 days. 2 Furhermore, he erm premium is assumed o be consan and capured by he residual in he regression. The perfec foresigh assumpion can be removed by replacing he realized funds raes wih expecaions derived from, for example, federal funds fuures conracs on he righ hand side. The appendix describes he calculaion of daily expecaions over he nex niney days based on federal funds fuures conracs. Expressing equaion (1) in firs differences gives us: 1 TB 3 FFR E ( FFR 1) E ( FFR 2)... E ( FFR 90) 90 (2) In equaion (2), he erm premium drops due o differencing, under he assumpion ha i changes only a negligible amoun from one day o anoher, which is an even weaker assumpion han a consan erm premium hroughou he mauriy of he long-erm conrac. This specificaion is paricularly convenien for our purposes because i allows us o invesigae he imporance of imposing he perfec foresigh assumpion and is implicaions in esing he expecaions hypohesis wihou worrying abou he erm premium. The firs column in Table 1 shows he resuls from he regression where changes in he hree-monh rae are regressed ono changes in he realized funds rae over he nex 90 days, as is ypically assumed in he lieraure. The sample period exends from January 1, 1990 hrough Sepember 15, The purpose of his exercise is o re-esimae a wellacceped specificaion from he erm srucure lieraure and use i for comparison in he laer analysis. Noe ha he slope coefficien is significanly differen from is heoreical value of 2 More specifically, he ess check wheher he spread beween oday s 90-day Treasury rae and he funds rae help explain he spread beween he average funds rae over he nex 90 days and oday s funds rae. 5

8 one and he 2 R is very low. Insead, he second column shows he regression resuls where he change in he hree-monh rae is regressed ono he expeced changes in he funds rae over he nex 90 days. Expeced changes in he funds rae over he nex 90 and 180 days are derived from federal funds fuures conracs. The appendix describes our mehodology of deriving longer erm policy expecaions in his manner. This ime, he coefficien esimae is insignificanly differen from is heoreical value of one. Furhermore, he regression increases noiceably. 2 R of he The hird and fourh columns in Table 1 show he resuls from a similar exercise wih changes in six-monh Treasury yield regressed ono he change in he average funds rae in he nex six monhs and he change in he average expeced funds rae in he nex six monhs. The resuls are similar o he resuls for he hree-monh bill rae. When he expeced funds rae is used insead of he realized funds rae, he coefficien esimae equals is heoreical value of one and 2 R increases subsanially. Marke expecaions of he funds rae over he fuure monhs can also be derived from he overnigh-indexed swap (OIS) rae. Overnigh indexed swaps are over-he-couner raded derivaives in which one pary agrees o pay a fixed rae in exchange for he average of a floaing cenral-bank rae over he life of he swap. For dollar swaps, he floaing rae is he daily effecive federal funds rae. The OIS rae is a measure of marke paricipans expeced average federal funds rae over he relevan erm. One drawback, however, is ha daa on overnigh-indexed swaps were no available prior o December 2001 because he marke was sill developing. In conras, he measure of expecaions ha we used in Table 1 goes back o 1989 and allows for a longer sample. Table 2 illusraes how he resuls based on federal funds fuures conracs compare o hose based on OIS raes. The firs column in Table 2 replicaes he firs column Table 1 for he sample afer December 2001 where he hreemonh Treasury bill rae is regressed ono he average funds rae over he nex 90 days. The 6

9 coefficien esimae is comparable o he one obained for he longer sample and is significanly smaller han one. The second and hird columns replace he average funds rae wih he expeced funds rae based on federal funds fuures conracs and hree-monh OIS rae respecively. In boh cases, he coefficien esimae associaed wih he expeced funds rae is insignificanly differen from is heoreical value of one. The close resemblance beween he resuls using eiher expecaions measure is consisen wih he discussion in he Appendix regarding he close mach beween he wo expecaions measures. Term premiums and bank funding raes The resuls presened in he previous secion sugges ha esimaion of he expecaions hypohesis a he near end of he yield curve is sensiive o he use of realized raes versus marke-based expecaions of fuure shor raes. Using marke-based measures of expeced raes produces resuls where he expecaions hypohesis appears o hold a he shor end of he yield curve. This finding suggess ha he previously esablished resuls regarding he weak evidence in favor of he expecaions hypohesis arise from he inappropriae proxy used for marke expecaions. When proper measures of expecaions are used insead, he evidence srongly suppors he expecaions hypohesis. We now urn o sudying he erm premium and analyze is behavior during he curren crisis. The esimaion in he previous secion was done in changes, following much of he lieraure, o avoid poenial issues of nonsaionariy wih he ineres raes and o avoid he erm premium. The level of raes, or more precisely, he level of he erm rae relaive o he expeced overnigh rae, however, may also be of ineres. Term spreads are ypically hough o capure risk premiums, and esimaing erm-srucure relaionships from spreads are a way o avoid saionariy problems. Tha said, in he simples form, using a erm spread as he dependen variable and esimaing he effec of oher variables on ha spread essenially 7

10 imposes he expecaions hypohesis on he daa. Esimaing he relaionship in levels o be able o es he hypohesis is valid if residuals from he regression are saionary, implying ha here is a coinegraing relaionship in he nonsaionary variables. Furhermore, esimaing he regression in levels allows us o quanify he componens of his erm premium and beer undersand he reasons behind ineres rae flucuaions during he recen financial urmoil. While he resuls of he previous secion appear o be supporive of he expecaions hypohesis, he comparison of he federal funds rae an unsecured, bank funding rae o he Treasury bill rae a riskless, governmen funding rae may be a bi problemaic especially when we consider he variables in levels. Spreads beween hese raes will likely reflec risk premiums ha we would expec, bu because he insrumens are inherenly differen and he markes have differen paricipans, he comparison is no direc. To make a more direc comparison, we use differen bank funding raes, hree-monh Libor, hree-monh Eurodollar, and hree-monh federal funds o es he expecaions hypohesis. We run he same esimaion using he hree-monh Treasury bill rae as a comparison. In he level regressions, he dependen variable is one of he erm raes. According o he expecaions hypohesis, he erm rae should equal expeced shor rae over he mauriy of he erm rae and a erm premium. In order o capure he expecaions componen we use he OIS rae or he expeced funds rae derived from federal funds fuures conracs as an independen variable. In his simple specificaion, he residuals are non-saionary, suggesing ha he coinegraing relaionship, if i exiss, has no been capured. Adding a measure of federal funds volailiy o capure par of he erm premium, we obain a co-inegraing relaionship ha gives saionary residuals. To compare he resuls o oher research, we also include a measure of credi risk, alhough he laer alone is no sufficien o generae saionary errors in he absence of a measure for federal funds volailiy. 8

11 Table 3 presens he resuls of benchmark regressions. Here, we sar our sample period in January 2001 o be able o use CDS spreads for large banks as a measure of credi risk. Taylor and Williams (2009) use he median five-year CDS annual rae for he banks in he US dollar Libor survey saring in Imporanly, his sample includes relaively calm periods in he bank funding marke as well as some raher urbulen episodes. In he upper panel (panel A), we regress he level of he erm rae on a consan, comparable mauriy OIS rae, he realized volailiy of he federal funds rae, and he median CDS spread for large banks. This is our benchmark specificaion. The las wo erms are inended o capure he erm premium. Volailiy in he federal funds marke can be measured in differen ways. In hese resuls, we show he resuls from using he average inraday volailiy over he preceding 30 days as a proxy for expeced volailiy in he near fuure. However, he resuls are robus o using oher measures of funds rae volailiy, such as realized daily sandard deviaion of he federal funds rae or he mean absolue deviaion of he funds rae from he arge over he prior 30 days (no shown). If he expecaions hypohesis were o hold perfecly, he consan erm would equal a ime-invarian erm premium and he slope on he OIS rae would equal one. Column 1 in he upper panel of Table 3 shows ha for hree-monh Libor, he coefficien on he OIS rae is very close o one. 3 The coefficien, however, is raher precisely measured and is saisically significanly differen from one. The median CDS spread has a posiive and saisically significan coefficien, confirming he resuls in oher research ha, condiional on a given level of he expeced pah for he funds rae, greaer credi risk among banks is associaed wih a wider erm premium. Volailiy in he federal funds marke is also saisically significan and associaed wih a wider erm premium. Finally, he R-squared of he regression is very high. The high R-squared, however migh lead one o suspec ha he 3 One day forward Libor rae is used in he regressions o adjus for he ime difference beween New York and London. 9

12 regression is subjec o spurious correlaion, given he fac ha ineres raes are ypically found o be nonsaionary. However, he saionariy of he residuals, and hus he presence of he coinegraing relaionship, implies ha he regression is valid and he coefficiens are esimaed consisenly. Wha does he firs column of resuls ell us? Essenially, he slope coefficien suggess ha he expecaions hypohesis basically holds for bank funding markes from he overnigh rae o he hree-monh rae. The erm premium, however, is imporanly linked o credi risk. This resul should be unsurprising, as many sudies of he Libor-OIS spread during he curren financial crisis have found a robus correlaion beween he spread and CDS spreads, oher measures of credi risk, and oher measures of liquidiy risk, see for example Schwarz, 2009, Taylor and Williams, 2009, and Chrisensen, Lopez, and Rudebusch, Oher researchers have examined he role risk or cenral bank inervenion has played in deermining he Libor-OIS spread. Wha is novel here, is he fac ha he volailiy in he federal funds rae is also saisically and economically significan. During normal imes, volailiy in he federal funds rae is around 5 basis poins. During he financial crisis, average monhly inraday volailiy go as high as 90 basis poins, implying ha his volailiy could be responsible for as much as 278 (= ) basis poins of he Libor-OIS spread. Figure 2 plos he Libor-OIS spread, he fied value from our regression, and he spread ha our model suggess is aribuable o federal funds volailiy. Of noe, following year end 2008, volailiy in he federal funds rae declined noably and he Libor-OIS spread narrowed even more. To be sure, general marke condiions improved, however, he abiliy of a bank ha migh be inclined o arbirage erm markes was clearly enhanced by greaer cerainy over he pah of he funds rae. Columns 2 and 3 provide robusness checks and presen a similar picure for he hreemonh Eurodollar rae and he hree-monh federal funds rae. Qualiaively, he resuls are 10

13 virually idenical. The slope coefficien is close o one, credi marke risk is a significan explanaory variable, and volailiy in he overnigh marke is saisically significan. The picure is a bi differen when he erm rae is he hree-monh Treasury bill rae. The coefficiens on CDS spreads and on federal funds rae volailiy are boh saisically significan, bu negaive. These resuls, however, are inuiive. The Treasury bill is a riskfree insrumen and, more imporanly, a safe-haven asse. When markes experience elevaed risk or volailiy, demand for he safes asses increases, driving down he yield on Treasury bills. The fac ha he coefficiens are of opposie signs, however, underscores he advanages of comparing like ypes of funding raes. As an addiional robusness check, we repea he analysis by replacing he OIS rae wih he measure of he expeced funds rae ha is derived from federal funds fuures conracs. As shown in he lower panel of able 3 (panel B), he resuls are essenially idenical, reflecing he fac ha our wo expecaions measures are very similar. This resul is reassuring because he federal funds fuures daa are available prior o 2001, allowing us o exend our sample period backwards and ye be confiden ha he resuls are no dependen on a single measure of expecaions. Taylor and Williams (2009) noe ha in addiion o credi-defaul-swap spreads, he spread beween he yen-denominaed Libor and Tibor, or he spread beween Libor and repo raes can be used as alernaive measures of counerpary risk. These measures of risk no only provide a robusness check for our resuls, hey also allow us o exend our sample period. In Table 4, we repea he analysis in Table 3 bu replace he CDS spread wih he Libor-Tibor spread. 4 The upper panel (panel A) uses he OIS rae as a measure of expecaions. Overall, he resuls are comparable o Table 3 alhough he credi risk measure has he opposie sign in he Eurodollar equaion and insignifican in he funds rae equaion. 4 Tibor rae is forwarded one period relaive o Libor in compuing he Libor-Tibor spread o adjus for he ime difference beween London and Tokyo. 11

14 In he lower panel (panel B), we replace he OIS rae wih he federal funds fuures based measure of expecaions and expand he sample period backwards o November When we ake advanage of a longer sample, all he coefficien esimaes become significan and heir values are comparable o hose in Table 3. The coefficien esimaes associaed wih he Libor-Tibor spread are significanly larger han hose associaed wih he CDS spread and he difference is saisically significan. Table 5 conemplaes ye anoher measure of counerpary risk considered in Taylor and Williams (2009). Insead of using he median CDS spread as we have considered in Table 3, we use an index of he CDS spread consruced by he Board of Governors. The resuls are comparable o he benchmark specificaion in Table 3. The main focus in Taylor and Williams (2009) is o analyze he effeciveness of he Term Aucion Faciliy in driving down he spread on erm lending raes. To ha end, hey es for he significance of dummy variables for he day of TAF aucions and each of he four days following he aucion. In order o check how heir resuls change afer we conrol for federal funds volailiy, we add dummy variables for TAF days ino our specificaion and adjus our sample period o mach wih heirs. While he coefficien esimaes for he TAF dummies are negaive, none of hem are significan (no shown). The lieraure has no reached an agreemen on how o measure he effeciveness of TAF. As an alernaive o Taylor and Williams (2009), Wu (2008) defined a TAF dummy ha equals zero before he TAF was firs inroduced on December 12, 2007, and one aferwards. 6 This specificaion assumes ha he TAF faciliy would permanenly reduce liquidiy risk affecing inerbank lending markes. Table 6 shows he resuls from he specificaion using his dummy variable. As shown, he TAF dummy is negaive and highly significan for all erm raes. While we do 5 Tibor daa is available afer November 1995, which deermines he beginning of he sample size in panel B. 6 In our specificaion he TAF dummy akes he value of one beween 12/17/2007 and 9/15/

15 no ake a sand on he inerpreaion of hese ypes of analyses, our main resuls are robus o he inclusion of hese measures. We conclude ha, however effecive he TAF was in narrowing spreads and lowering raes, he role of volailiy in he funds marke also needs o be considered. Robusness Analysis One quesion regarding he inerpreaion of our resuls is wheher he impac of inraday volailiy on he erm premium is driven by he exraordinary flucuaions in his variable during he crisis period. In order o conrol for he crisis, we generae a dummy variable ha capures he crisis period and inerac his dummy variable wih inraday volailiy in our benchmark specificaion. 7 Table 7 shows he resuls from his analysis. As shown, inraday volailiy is significan boh before and afer he crisis. The difference beween he wo periods is saisically insignifican for mos raes excep for he Treasury rae. For he Treasury rae, he volailiy eners wih a negaive sign only during he crisis period, suggesing ha he volailiy in he crisis affeced ha marke differenly. One way o reconcile our resuls wih he liquidiy premium heory is o noe ha inraday volailiy may a leas parially capure he liquidiy risk componen of he erm premium. This way of inerpreing our resuls would go agains Taylor and Williams (2009) argumen ha he Libor-OIS spread should no conain any liquidiy risk. In order o es his argumen more horoughly we add addiional measures of liquidiy risk o our benchmark specificaion such as he spread beween he six-monh and hree-monh Treasury bill raes and he volume in he federal funds marke. Furhermore, in order o conrol for poenial spillovers beween he major financial markes, we also add he volailiy measured in he 7 The dummy variable akes he value fo 1 from Augus 9, 2007 hrough he end of our sample on Sepember 15,

16 Euro area and UK. 8 Table 8 shows he resuls from his exercise. Two observaions are noiceable. Firs, he addiional liquidiy risk measures are highly significan in mos of he regressions. From a heoreical perspecive, Eisenschmid and Tapking (2009) reached a similar conclusion for he Euro area, arguing ha he raes in he inerbank markes could no be explained wih credi risk alone and he liquidiy risk should play a role. Second, inraday volailiy is sill significan even in he presence of he addiional liquidiy measures. Finally, inraday volailiies in he Euro area and he UK are generally significan in affecing he money marke raes in he US boh in he period before and afer he crisis. As a final robusness es, we check for GARCH effecs. We show he resuls for he Libor equaion in Table 9. Inraday volailiy is significan for he mean equaion before and afer he crisis. Meanwhile, measures of credi and liquidiy risk have a negaive impac on he variance of Libor. 9 An Exension for he Euro Area and he UK So far we have esablished he role of volailiy on shor erm ineres raes in he US. In his secion, we exend our analysis o he Euro Area and he UK. The firs column in Table 10 shows he resuls for he Euro Area where he benchmark specificaion is esimaed for his region. Here, Libor is replaced by Euribor and he hiry-day railing sandard deviaion of he Eonia is used as a measure for volailiy. The second column adds inraday volailiy in he US and he UK o he Euribor equaion before and afer he crisis. Eonia volailiy is significan in affecing Euribor similar o our resuls for he US. However, he impac of volailiy afer he crisis is significanly differen from is impac before he crisis. Furhermore, volailiy in he US as well as he UK are significan in affecing Eonia boh 8 Volailiy in bank funding markes in he Euro area and he UK are measured by he sandard deviaions in he overnigh lending raes in hese regions (Eonia and Sonia respecively) over he las 30 days. 9 For furher robusness checks, we consider adding a dummy variable o conrol for volailiy on quarer-ends (McAndrews e al. (2009) which urns ou o be insignifican (no shown). 14

17 before and afer he crisis as well, alhough heir significance increases dramaically during he crisis. The spread beween he six-monh and hree-monh German bond raes, which is added as an addiional measure of liquidiy risk, is insignifican. Table 11 checks for he presence of GARCH effecs. Mos of he regressors ha are significan in he mean equaion are also significan in he variance equaion. US volailiy has a larger impac on he mean equaion for Euribor relaive o Eonia volailiy during he crisis period. Tables 12 and 13 are he counerpars of Tables 10 and 11 for he UK. This ime, he dependen variable is Serling-denominaed Libor. As he addiional measure of liquidiy risk, we use he spread beween he hree monh and overnigh repo raes. The resuls are very similar o hose obained for he Euro Area. Own overnigh volailiy as well as foreign overnigh volailiies are significan in deermining he erm premium which is more pronounced afer he crisis. Evidence of GARCH effecs are deeced in he variance equaion. Conclusions The resuls presened above have a variey of implicaions. Firs, he resuls provide anoher se of evidence ha he expecaions hypohesis is generally a valid characerizaion of he erm srucure of ineres raes, a leas a he very near end of he yield curve. In erms of levels, a higher degree of volailiy in he overnigh rae is associaed wih a greaer erm premium. Tha is o say, greaer volailiy leads o a higher longer-erm rae for a given level of he shor rae. If one mechanism hrough which he expecaions hypohesis holds is ineremporal arbirage, lenders lending long while funding hemselves shor, volailiy in he shor rae increases he risk associaed wih his rade, making he lender demand a higher erm premium. 15

18 The implicaions of hese findings are varied. Failure o find empirical suppor for he expecaions hypohesis could reflec mismeasuremen of expecaions, no simply a refuaion of he hypohesis. Our resuls confirm ha using measures of he expeced federal funds rae insead of he realized federal funds rae yields resuls ha end o suppor he expecaions hypohesis. Second, in he curren financial crisis, a grea deal of aenion has been paid o he Libor-OIS spread. The popular view is ha his spread reflecs liquidiy and erm premiums in he bank funding marke, and hus he spread can be used as a summary saisic for hose srains. Those effecs are surely presen, however hese resuls sugges also considering he volailiy in he overnigh rae when inerpreing ha spread. Essenially, he higher volailiy adds o he liquidiy risk ha exiss in he marke. This resul is rue for he US as well as he Euro Area and he UK. Furhermore, inerbank volailiy in one marke has spillovers in oher markes. Finally, he Federal Reserve has changed is operaing procedure for he daily implemenaion of moneary policy. The high level of reserve balances in he banking sysem has led o a discussion of various ools a he cenral bank s disposal for is exi sraegy from is curren accomodaive sance. If hose ools lead o an operaing framework where he overnigh rae is more volaile han i had been, even condiional on being able o hi a arge rae on avearge, hen he resuls presened above sugges ha erm premiums should be higher and, all else equal, longer-erm ineres raes will be higher condiional on a given seing of he overnigh rae. 16

19 References Benne, P., and Perisiani, S., 2002, Are U.S. Reserve Requiremens Sill Binding?, Federal Reserve Bank of New York Economic Policy Review 8, no. 1, Bernanke, B., and Blinder, A., 1992, The Federal Funds Rae and he Channels of Moneary Transmission, American Economic Review 82(4), Campbell, J.Y., and Shiller, R.J., 1991, Yield Spreads and Ineres Rae Movemens: A Bird s Eye View, Review of Economic Sudies 58, Carpener, S., and Demiralp, S., 2006, Anicipaion of Moneary Policy and Open Marke Operaions, Inernaional Journal of Cenral Banking June, Chrisensen, J. H. E., Lopez, J.A., and Rudebusch, G.D., 2009, Do Cenral Bank Liquidiy Faciliies Affec Inerbank Lending Raes?, FRBSF Working Paper (June). Cook, T., and Hahn, T., 1989, The Effec of Changes in he Federal Funds Rae on Marke Ineres Raes in he 1970s, Journal of Moneary Economics 24, Demiralp, S., 2008, Moneary Policy Surprises and he Expecaions Hypohesis a he Shor End of he Yield Curve, Economics Leers, 101: 1-3. Demiralp, S., Farley, D., 2005, Declining required reserves, funds rae volailiy, and open marke operaions, Journal of Banking and Finance 29, Eisenschmid, J., Tapking, J., 2009, Liquidiy risk premia in unsecured inerbank money markes, European Cenral Bank Working Paper No: Gurkaynak, R., Sack, B. and Swanson, E., 2007, Marke-Based Measures of Moneary Policy Expecaions, Journal of Business and Economic Saisics 25(2), April, Hilon, S., 2005, Trends in Federal Funds Rae Volailiy, Curren issues in Economics and Finance, Federal Reserve Bank of New York, July 2005 Volume 11, Number 7 Kuner, K., Moneary Policy Surprises and Ineres Raes: Evidence from he Fed Funds Fuures Marke, Journal of Moneary Economics,47, Lange, J., Sack, B., and Whiesell, W., 2003, Anicipaions of Moneary Policy in Financial Markes, Journal of Money, Credi, and Banking 35, Mankiw, N.G., and Miron, J.A., 1986, The Changing Behavior of he Term Srucure of Ineres Raes, Quarerly Journal of Economics 101, McAndrews, J., Sarkar, A., and Wang, Z., 2008, The Effec of he Term Aucion Faciliy on he London Iner-Bank Offered Rae, FRB New York Saff Repor 335(July). Meulendyke, A. M., 1998, U.S. Moneary Policy and Financial Markes, New York, Federal Reserve Bank of New York. Nauz, D., Schmid, S., Moneary policy implemenaion and he federal funds rae. Journal of Banking and Finance 33,

20 Rudebusch, G., 1995, Federal Reserve Ineres Rae Targeing, Raional Expecaions, and he Term Srucure, Journal of Moneary Economics 35, Schwarz, K., 2009, Mind he Gap: Disenangling Credi and Liquidiy in Risk Spreads, Columbia Universiy, unpublished manuscrip Shiller, R.J., Campbell, J.Y., and Schoenholz, K.L., 1983, Forward Raes and Fuure Policy: Inerpreing he Term Srucure of Ineres Raes, Brookings Papers on Economic Aciviy no. 1, Taylor, J., and Williams, J., 2009, A Black Swan in he Money Marke, American Economic Journal: Macroeconomics 1(1), Wu, T., 2008, On he Effeciveness of he Federal Reserve s New Liquidiy Faciliies, Federal Reserve Bank of Dallas Working Paper

21 Table 1: Tesing he Expecaions Hypohesis TB3 TB6 1/1/90-6/18/10 1/1/90-3/22/10 I II III IV Consan 0.00** ** Avg( FFR ) ** ** E Avg( FFR90 ) ** ** Adjused R Number of Obs saisics (based on Whie heeroskedasiciy consisen sandard errors) are below he coefficien esimaes. */** indicaes significance a 90%/95% level of significance. Realized average funds rae for TB3 (TB6) equaion is calculaed over he nex 90 (180) days. Expeced average funds rae ( Avg(FFR ) E ) for he TB3 (TB6) equaion is calculaed from federal funds fuures conracs over he nex 90 (180) days as described in he appendix. Table 2: Tesing he Expecaions Hypohesis wih Alernaive Measures of Expecaions Sample Period: 12/4/2001-6/18/2010 Dependen variable: TB3 I II III Consan Avg( FFR ) E Avg( FFR90 ) ** OIS (Three monh) ** 6.46 Adjused R Number of Obs saisics (based on Whie heeroskedasiciy consisen sandard errors) are below he coefficien esimaes. */** indicaes significance a 90%/95% level of significance. 19

22 Table 3: Tesing he Expecaions Hypohesis for various Ineres Raes Panel A: Using OIS rae as a measure of expecaions Sample Period: 12/4/2001-9/15/2010 I II III IV Libor ED Term FFR T-Bill 1. Consan -0.12** -0.30** -0.20** 0.12** OIS (3-monh) 0.99** 0.98** 0.97** 0.92** Inraday Vol. 3.09** 4.21** 3.89** -0.99** CDS (median) 0.33** 0.61** 0.42** -0.10** Adjused R Number of Obs Panel B: Using federal funds fuures based measure of expecaions Sample Period: 12/4/2001-9/15/2010 I II III V Libor ED Term FFR T-Bill 1. Consan -0.11** -0.28** -0.19** 0.13** 2. E Avg(FFR ) ** 0.99** 0.98** 0.93** Inraday Vol. 3.14** 4.24** 3.91** -0.97** CDS (median) 0.32** 0.60** 0.41** -0.10** Adjused R Number of Obs saisics (based on Whie heeroskedasiciy consisen sandard errors) are below he coefficien esimaes. */** indicaes significance a 90%/95% level of significance. One day forward Libor rae is used in he regressions o adjus for he ime difference beween New York and London. E Avg(FFR ) is he expeced funds rae calculaed from federal fund fuures conracs over he mauriy of he securiy (which is 90-days for all he securiies considered in his able). The mauriies for he Libor, Eurodollar, Term fed funds, and Treasury Bills are hree monhs. 20

23 Table 4: Tesing he Expecaions Hypohesis using Libor-Tibor spread as a measure of risk Panel A: Using OIS rae as a measure of expecaions Sample Period: 12/4/2001-9/15/2010 I II III IV Libor ED Term FFR T-Bill 1. Consan 0.19** 0.10** 0.09** OIS (3-monh) 0.92** 0.89** 0.90** 0.95** Inraday Vol. 3.27** 5.32** 4.54** -0.95** Libor-Tibor 0.66** -0.44** ** Adjused R Number of Obs Panel B: Using federal funds fuures based measure of expecaions Sample Period: 11/14/1995-9/15/2010 I II III IV Libor ED Term FFR T-Bill 1. Consan 0.28** 0.40** 0.29** -0.01** E 0.93** 0.87** 0.91** 0.96** Inraday Vol. 2.18** 2.94** 2.77** -0.56** Libor-Tibor 1.03** 1.44** 1.11** -0.39** Adjused R Number of Obs Avg(FFR) -saisics (based on Whie heeroskedasiciy consisen sandard errors) are below he coefficien esimaes. */** indicaes significance a 90%/95% level of significance. One day forward Libor rae is used in he regressions o adjus for he ime difference beween New York and London. Similarly, Tibor rae is forwarded one period relaive o Libor in compuing he Libor-Tibor spread o adjus for he ime difference beween London and Tokyo. E Avg(FFR ) is he expeced funds rae calculaed from federal fund fuures conracs over he mauriy of he securiy (which is 90-days for all he securiies considered in his able). Tibor daa is available afer 1995, which deermines he beginning of he sample size in panel B. The mauriies for he Libor, Eurodollar, Term fed funds, and Treasury Bills are hree monhs. 21

24 Table 5: Tesing he Expecaions Hypohesis using CDS index as a measure of risk Sample Period: 12/4/2001-9/15/2010 I II III IV Libor ED Term FFR T-Bill 1. Consan -0.14** -0.35** -0.24** 0.11** OIS (3-monh) 0.99** 0.99** 0.98** 0.93** Inraday Vol. 3.05** 4.09** 3.81** -1.01** CDS index 0.32** 0.62** 0.43** -0.08** Adjused R Number of Obs saisics (based on Whie heeroskedasiciy consisen sandard errors) are below he coefficien esimaes. */** indicaes significance a 90%/95% level of significance One day forward Libor rae is used in he regressions o adjus for he ime difference beween New York and London. Table 6: Tesing he effeciveness of TAF Sample Period: 1/3/2007-6/4/2009 I II III IV Libor ED Term FFR T-Bill 1. Consan -0.51** -0.64** -0.54** 0.08** OIS (3-monh) 1.03** 1.01** 1.01** 0.92** Inraday Vol. 3.32** 4.48** 4.11** -0.95** CDS index 0.64** 0.89** 0.67** -0.05** TAF dummy -0.16** -0.16** -0.10** -0.01** Adjused R Number of Obs saisics (based on Whie heeroskedasiciy consisen sandard errors) are below he coefficien esimaes. */** indicaes significance a 90%/95% level of significance One day forward Libor rae is used in he regressions o adjus for he ime difference beween New York and London. The mauriies for he Libor, Eurodollar, erm fed funds, and Treasury Bills are hree monhs. 22

25 Table 7: Robusness Analysis I Sample Period: 12/4/2001-9/15/2010 I II III IV Libor ED Term FFR T-Bill 1. Consan ** -0.25** -0.18** -0.06** OIS (3-monh) 0.99** 0.99** 0.97** 0.91** Inraday Vol. (1 D ) 2.64** 3.40** 3.42** 2.24** Inraday Vol. D 3.07** 4.17** 3.87** -0.84** CDS_median 0.31** 0.57** 0.40** 0.03** Adjused R Number of Obs saisics (based on Whie heeroskedasiciy consisen sandard errors) are below he coefficien esimaes. D akes he value of 1 beween Augus 9, 2007 hrough Sepember 15,

26 Table 8: Robusness Analysis II Sample Period: 12/4/2001-9/15/2010 I II III IV Libor ED Term FFR T-Bill 1. Consan -1.34** ** 1.80** OIS (3-monh) 1.00** 0.98** 0.98** 0.91** Inraday Vol. (1 D ) 1.11** 2.40** 2.00** 2.84** Inraday Vol. D 1.98** 2.71** 2.51** -0.51** CDS_median 0.30** 0.47** 0.34** -0.09** TB6-TB3 0.49** 0.70 ** 0.62** -0.54** FF Volume 0.10** ** -0.16** Eonia Vol. (1 D ) 0.45** 0.62** 0.49** D 9. Eonia Vol. 0.25** 0.58** ** Sonia Vol. (1 D ) 0.14** -0.13** ** Sonia Vol. D 1.00** 1.42** 1.45** 0.11** Adjused R Number of Obs saisics (based on Whie heeroskedasiciy consisen sandard errors) are below he coefficien esimaes. 24

27 Table 9: GARCH Effecs for he US Sample Period: 12/4/2001-9/15/2010 Dependen Variable: Libor (3-monh) I II Mean Equaion Variance Equaion 1. Consan -1.23** 0.01** OIS (3-monh) 0.99** -0.00** Inraday Vol. (1 D ) 0.60** D 4. Inraday Vol. 1.41** 0.01** CDS_median 0.08** -0.00** TB6-TB3 0.08** -0.00** FF Volume 0.11** -0.00** Eonia Vol. (1 D ) 0.07** Eonia Vol. D 0.37** -0.01** Sonia Vol. (1 D ) 0.07** -0.00** Sonia Vol. D 1.28** 0.01** Residual ** GARCH ** Adjused R Number of Obs z-saisics (based on Bollerslev-Wooldrige robus sandard errors & covariance) are shown below he coefficien esimaes. */** indicaes significance a 90%/95% level of significance 25

28 Table 10: Tesing he Expecaions Hypohesis for he Euro Area using median CDS as a measure of Expecaions Sample Period: 1/2/2001-9/15/2010 Dependen Variable: Euribor (3-monh) I II 1. Consan -0.12** 0.04** OIS (3-monh) 1.06** 1.00** Eonia Vol. (1 D ) -0.39** 0.07** Eonia Vol. D 2.62** 0.83** CDS (median) 0.22** 0.15** German Bond (6m)-German Bond (3m) Inraday Vol. (1 D ) * D 8. Inraday Vol ** Sonia Vol. (1 D ) ** Sonia Vol. D ** Adjused R Number of Obs saisics (based on Whie heeroskedasiciy consisen sandard errors) are below he coefficien esimaes. */** indicaes significance a 90%/95% level of significance 26

29 Table 11: GARCH Effecs for he Euro Area Sample Period: 1/2/2001-9/15/2010 Dependen Variable: Euribor (3-monh) I II Mean Equaion Variance Equaion 1. Consan 0.06** 0.00** OIS (3-monh) 1.00** -0.00** STD_Eonia (1 D ) 0.05** -0.00** D 4. STD_Eonia 0.05** -0.01** CDS (median) 0.13** -0.01** German Bond (6m)-German Bond (3m) ** Inraday Vol. (1 D ) ** Inraday Vol. D 1.24** -0.00* Sonia Vol. (1 D ) -0.07** -0.00** Sonia Vol. D 0.83** 0.01** Residual ** GARCH R Number of Obs z-saisics (based on Bollerslev-Wooldrige robus sandard errors & covariance) are shown below he coefficien esimaes. */** indicaes significance a 90%/95% level of significance 27

30 Table 12: Tesing he Expecaions Hypohesis for he UK Sample Period:1/2/2001-9/15/2010 Dependen Variable: Serling denominaed Libor (3-monh) I II 1. Consan -0.18** -0.09** OIS (3-monh) 1.06** 1.03** Sonia Vol. (1 D ) -0.25** -0.04** Sonia Vol. ( D ) 2.29** 1.44** CDS (median) 0.50** 0.27** RP(3m)-RP(ON) ** Inraday Vol. (1 D ) ** Inraday Vol. D ** Eonia Vol. (1 D ) ** Eonia Vol. D ** Adjused R Number of Obs saisics (based on Whie heeroskedasiciy consisen sandard errors) are below he coefficien esimaes. */** indicaes significance a 90%/95% level of significance 28

31 Table 13: GARCH Effecs for he UK Sample Period: 1/2/2001-9/15/2010 Dependen Variable: Serling Denominaed Libor (3-monh) I II Mean Equaion Variance Equaion 1. Consan -0.07** 0.01** OIS (3-monh) 1.03** -0.00** Sonia Vol. (1 D ) -0.02** -0.00** Sonia Vol. ( D ) 1.52** 0.06** CDS (median) 0.14** -0.00** RP(3m)-RP(ON) 0.01** -0.00** Inraday Vol. (1 D ) 0.04** -0.02** Inraday Vol. D 1.27** Eonia Vol. (1 D ) 0.12** -0.01** Eonia Vol. D 1.46** -0.04** Residual ** GARCH Adjused R Number of Obs z-saisics (based on Bollerslev-Wooldrige robus sandard errors & covariance) are shown below he coefficien esimaes. */** indicaes significance a 90%/95% level of significance 29

32 Figure 1: The Libor-OIS Spread over he Course of he Percen Libor-OIS Median CDS Average Inraday Volailiy 30

33 Figure 2: Prediced Libor-OIS spread Percen Libor-OIS Spread Prediced Spread Spread due o funds rae volailiy Prediced Spread=(Prediced Libor from Table 3, column 1)-OIS Spread due o FFR volailiy= ^ Vol FFR Volailiy 31

34 Appendix: Calculaion of 90-day Expecaions The following diagram illusraes our logic in calculaing 90-day expecaions 1 2 k A B C D where 1: he curren day m i : he number of days in monh i 2 : he number of days included from he 4h monh m m ( m ) ( ) k : day of FOMC meeing in monh 4. A: Average expeced funds rae in he remaining days of he curren monh B: Average expeced funds rae in monh 2 C: Average expeced funds rae in monh 3 D: Average expeced funds rae unil 2 in monh 4 We now describe how we calculae each of hese componens A hrough D. A: Average expeced funds rae in he remaining days of he curren monh On day, spo monh fuures conrac ( FF1 ) reflecs he expeced funds rae for he curren monh. Tha is: FF1 1 E m 1 m 1 i1 FFR i (A.1) where m 1 is he oal number of days in monh 1 (curren monh), E is he expecaions operaor based on informaion as of day, FFR is he effecive funds 32