Y2K Options and the Liquidity Premium in Treasury Markets

Transcription

1 Y2K Opions and he Liquidiy Premium in Treasury Markes Suresh Sundaresan Columbia Universiy Zhenyu Wang Federal Reserve Bank of New York Financial insiuions around he world expeced he millennium dae change (Y2K) o cause an aggregae liquidiy shorage. Responding o he concern, he Federal Reserve Bank of New York aucioned Y2K opions o primary dealers. The opions gave he dealers he righ o borrow from he Fed a a predeermined ineres rae. Using he implied volailiies of Y2K opions and he on/off-he-run spread, we demonsrae ha he Fed s acion eased he fears of bond dealers, conribuing o a drop in he liquidiy premium of Treasury securiies. Our analysis shows he link beween he microsrucure of governmen deb markes and he cenral bank s provision of liquidiy. We argue ha Y2K opions and heir effecs on liquidiy premium broadly conform o he economic heory on public provision of privae liquidiy. (JEL G1, G12, G18) The Millennium Dae Change (usually referred o as Y2K or someimes as Cenury Dae Change) was viewed, ex ane, as a period of poenial aggregae liquidiy shorage. Liquidiy or ready access o funds is paramoun o he survival of firms and financial inermediaries such as governmen bond dealers. Liquidiy is especially paramoun when an aggregae shock (or aggregae uncerainy) hreaens he overall economy. The liquidiy premium and he supply-demand of liquidiy ahead of Y2K are he focus of our inquiry. Responding o he concern of liquidiy shorage around Y2K, he Federal Reserve Bank of New York aucioned opions ha gave he bond dealers he righ o borrow from he Fed a a predeermined rae. To our knowledge, his is he firs ime ha he Fed sold such opions for managing a perceived aggregae liquidiy risk. We will refer o hese opions as Y2K opions hroughou he The auhors are indebed o he anonymous referee for suggesions and appreciae commens from Viral Acharya, Tobias Adrian, B. P. A. Andrews, Sudipo Bhaacharya, Ulrich Bindseil, Michael Fleming, Ken Garbade, Lorenzo Garlappi, Spence Hilon, Berng Holmsrom, Arvind Krishnamurhy, Owen Lamon, Francis Longsaff, Asani Sarkar, and paricipans of seminars and conferences where he paper was presened. The auhors are graeful o he Federal Reserve Bank of New York for providing he daa on he aucion of Y2K opions and Spence Hilon for helping us wih he daa. Sundaresan acknowledges Columbia Business School summer research gran and research grans from J. P. Morgan and Moody s Invesmen Service. Bre Dunn, Alexis Iwanisziw, and Michal Lemenowski have provided excellen research assisance. The views saed here are hose of he auhors and do no necessarily reflec he views of he Federal Reserve Bank of New York or he Federal Reserve Sysem. Send correspondence o Suresh Sundaresan, Uris Hall, Room 811, 3022 Broadway, New York, NY 10027, elephone: ms122@columbia.edu. Downloaded from hp://rfs.oxfordjournals.org a Columbia Universiy Libraries on Augus 3, 2010 C The Auhor Published by Oxford Universiy Press on behalf of The Sociey for Financial Sudies. All righs reserved. For Permissions, please journals.permissions@oxfordjournals.org. doi: /rfs/hhn005 Advance Access publicaion February 28, 2008

2 The Review of Financial Sudies / v 22 n paper. By selling hese Y2K opions, he cenral bank commied a large amoun of liquidiy o he Treasury bond markes. Our goal here is o use his unique even o gain insighs ino he relaionship beween he acions of he cenral bank and he liquidiy premium in he Treasury bond markes. Through he even of Y2K and Y2K opions, we show he link beween he liquidiy premium of governmen deb and he cenral bank s provision of liquidiy. Using he implied volailiies of Y2K opions and he spread beween he off-he-run and on-he-run Treasury bonds, we demonsrae ha he Fed s acion eased he fears of Treasury bond dealers. The ease of fear conribued o a drop in he liquidiy premium of Treasury securiies. We argue ha he issuance of Y2K opions and heir effecs on liquidiy premium is in broad conformiy wih he economic heory on public provision of privae liquidiy. Our paper proceeds as follows. In Secion 1, we discuss he naure of he Y2K problem and describe he Fed s issuance of Y2K opions o deal wih he problem. In Secion 2, we analyze he implied volailiies of Y2K opions and he aggressiveness of demand for he cenral bank s provision of liquidiy. This analysis allows us o ge an assessmen of he marke s view of poenial shock in he period before he Y2K dae and o documen how he view changed from Ocober hrough December In Secion 3, we link Y2K opions o he liquidiy premium in he Treasury markes. Finally, in Secion 4, we inerpre he Fed s use of Y2K opions in he conex of received economic heory on public provision of privae liquidiy. We also discuss oher acions aken by he Fed, as well as acions aken by oher cenral banks. In Secion 5, we provide concluding remarks. 1. Background 1.1 Poenial liquidiy shorage around Y2K On he Y2K dae, financial insiuions faced he echnological risk ha heir own sysems would fail and cause operaional problems. Toward he end of he wenieh cenury, hese insiuions began o rely heavily, if no exclusively, on compuers o ransac business, keep records, and mainain securiy. Nearly every financial ransacion involves numerous compuer funcions. The Y2K problem originaed from a belief ha mos compuer sofware, using only he las wo digis o idenify he year, could misinerpre a ransacion dae in 2000 as one in Wih such misinerpreaion, ineres could be miscalculaed, sock rades could vanish, and cusomers could have difficuly accessing heir accouns or using heir credi and debi cards. This high level of echnological dependence made financial insiuions paricularly vulnerable o he Y2K problem. Beyond his echnological vulnerabiliy and perhaps more imporanly, financial insiuions also faced he risk ha heir counerparies would fail on he Y2K dae. Financial insiuions are known for heir inerconnecedness Downloaded from hp://rfs.oxfordjournals.org a Columbia Universiy Libraries on Augus 3,

3 Y2K Opions and Liquidiy Premium and dependence on heir counerparies for safe operaions. For example, a bank depends on is borrowers o repay loans in order o avoid losses. Financial insiuions rely on funding vehicles provided by oher insiuions o mainain adequae liquidiy. Because of his reliance on counerparies, financial insiuions faced he risk ha counerparies, borrowers, and cliens would succumb o Y2K problems, fail o mee heir obligaions, and cause losses. The counerpary risk could in urn cause liquidiy shorage around Y2K. In view of he counerpary risk, banks waned o shif selemens of forward ransacions away from Y2K. The poenial wihdrawal by a number of insiuions during his period may have discouraged rading, issuance, and invesmen during he Y2K ransiion. A signal of he shif of ransacions away from Y2K was visible in June 1999 when he erm spread beween he six-monh LIBOR and he hree-monh LIBOR more han doubled from a level of basis poins on June 28 o basis poins on June 30 (see Panel A in Figure 1). The implicaion was clear: lenders in he inerbank marke waned a premium o lend cash when he loan was due near Y2K. The erm spread coninued o widen o a level as high as basis poins as of Sepember 28, Then, he spread dropped precipiously by basis poins o basis poins 1 he nex day, due o he ballooning of he hree-monh LIBOR. This drop reflecs he fac ha he hree-monh LIBOR rae as of Sepember 29, 1999, applied o loans ha maured very close o he Y2K dae. We also see ha he erm spread revered o normal levels afer Y2K. The shif of ransacions also caused oher LIBOR erm spreads o jump. In Panel B of Figure 1, he erm spread beween hree-monh LIBOR and onemonh LIBOR sood a basis poins on Sepember 28, 1999, and hen more han quadrupled o basis poins on Sepember 29, The erm spread hen reached he level of basis poins on November 26, 1999, only o drop o a level of basis poins on November 29, Similar paerns occur in he spread beween he one-monh and one-week LIBOR raes (see Panel C). The spread jumped up one monh before Y2K and dropped one week before Y2K. Jumps relaed o he year-end dae happened only in 1999 bu no in oher years. In Panels D, E, and F of Figure 1, we plo he spread beween he six-monh and hree-monh LIBOR during 1996, 1997, and I is clear ha he changes of he spread a he end of Sepember in 1996, 1997, and 1998 were only small fracions of he change a he end of Sepember These graphs sugges ha he concern of he Y2K problem caused he large jumps in he LIBOR erm spread. The mos likely inerpreaion for he jumps is ha banks were relucan o make loans ha maured a he end of Downloaded from hp://rfs.oxfordjournals.org a Columbia Universiy Libraries on Augus 3, When comparing he jumps in erms of borrowing coss in dollars, we should conrol for he differences in he ime o mauriy of underlying deposis. 1023

4 The Review of Financial Sudies / v 22 n Figure 1 Term spreads in inerbank markes Panels A, B, and C plo he erm spreads among he one-week, one-monh, hree-monh, and six-monh LIBOR in Panels D, E, and F plo he erm spread beween he hree-monh and six-monh LIBOR in 1996, 1997, and (Source of daa: Federal Reserve Board and Briish Bankers Associaion.) The relucance o make loans ha would maure on or immediaely afer Y2K pushed up he commercial paper rae. From June o November 1999, he spread beween one-monh commercial paper and Treasury bill raes flucuaed beween 20 and 74 basis poins for nonfinancial and financial companies, as noed in Panels A and B of Figure 2. However, beginning on December 1, 1999, he spread for nonfinancial companies increased dramaically and reached a peak level of 116 basis poins on December 27. This is an increase of 84 basis poins from a spread of 32 basis poins on November 30. The spread for financial companies also increased dramaically in he las monh of I rose from 31 basis poins on November 30 o 114 basis poins on December 23. Clearly, shor-erm borrowing coss were higher han usual for loans ha were o maure immediaely afer Y2K. Downloaded from hp://rfs.oxfordjournals.org a Columbia Universiy Libraries on Augus 3,

5 Y2K Opions and Liquidiy Premium Figure 2 Shor-erm borrowing coss for corporaions This figure shows he shor-erm commercial borrowing raes during June 1, 1999 January 31, Panel A is he plo of he spread beween he raes of nonfinancial commercial paper and Treasury bills. Panel B is he plo of he spread beween financial commercial paper and Treasury bills. Panel C is he plo of he spread beween Eurodollar deposi and Treasury bills. (Source of daa: Federal Reserve Board and Briish Bankers Associaion.) The rise in borrowing cos was also evidenced in Eurodollar ime deposis (see Panel C of Figure 2), similar o he spreads of commercial paper over he Treasury bills. The spread beween he raes on one-monh Eurodollar ime deposis and Treasury bills flucuaed beween 20 and 77 basis poins during he period of June November The spread hen began o widen quickly on December 1 and reached a peak of 131 basis poins by December 8, The spreads remained a a high level unil December 28, 1999, and hen declined significanly hereafer. Clearly, due o counerpary risk, he cos of obaining liquidiy from money markes in he privae secor became prohibiively expensive during he period immediaely before Y2K. Downloaded from hp://rfs.oxfordjournals.org a Columbia Universiy Libraries on Augus 3,

6 The Review of Financial Sudies / v 22 n Counerpary risk was a major concern for he US cenral bank. Peer Fisher, hen Execuive Vice Presiden of he Federal Reserve Bank of New York, described his concern clearly: I seemed quie reasonable for cusomers and bankers o agree o shif selemens of forward ransacions away from he firs few days of January. However, we became more roubled by he escalaing effors, of a number of marke paricipans, o discourage normal rading, issuance, and invesmen aciviies during he Y2K ransiion. The desrucion of marke liquidiy implied by hese effors presened he risk of a self-fulfilling prophecy, whereby exreme risk aversion would creae expecaions and he realiy of excepionally hin marke condiions, making i more likely ha markes could be jarred by even a modes exernal shock Y2K relaed or oherwise. 2 In Augus 1999, he US cenral bank concluded ha Y2K migh lead o a liquidiy shorage if no acions were aken o preven i. The cenral bank was aware of he possibiliy ha cusomers and bankers migh agree o shif selemens of forward ransacions away from he Y2K period. I concluded ha he marke migh need poenially large year-end reserves. If dealers and financial inermediaries were o wihdraw from imporan markes, such as repurchase agreemens during his criical period, i would be challenging for he Fed o mee he need for liquidiy in a highly illiquid financing marke a year-end. 1.2 Opions issued by he US cenral bank The US cenral bank responded wih several policy iniiaives o mee he poenial aggregae liquidiy shorage, bu he mos imporan and innovaive iniiaives were he issuance of opions. The US cenral bank sold sae-coningen conracs, conracs wih erms explicily specified o be coningen on he liquidiy sae around Y2K. I was possible because Y2K represened one of he few foreseeable saes of poenial aggregae liquidiy shorage. 3 These conracs were opions ha allowed insiuional buyers o exercise and obain liquidiy in he presence of an aggregae liquidiy shock around Y2K. They were clearly argeed o mee he poenial shorage of liquidiy for banks and players in he Treasury bond marke. The insiuional arrangemen of Y2K opions and he inen of he Fed in issuing he opions are described in deail by Drossos and Hilon (2000). The res of his subsecion offers a brief overview of he opions. The firs iniiaive of issuing opions conracs was he Special Liquidiy Faciliy (SLF). The Federal Open Marke Commiee (FOMC) approved he iniiaive on July 20, 1999, more han five monhs ahead of Y2K. Under SLF, Downloaded from hp://rfs.oxfordjournals.org a Columbia Universiy Libraries on Augus 3, Source: Money Marke and he Cenury Dae Change, speech by Peer R. Fisher, Execuive Vice Presiden of he Federal Reserve Bank of New York, before he Money Markeeers of New York Universiy on December 1, Year-ends and major holidays are oher saes whose iming is known ahead. Seasonal agriculural needs for liquidiy are also relaively foreseeable. 1026

7 Y2K Opions and Liquidiy Premium he deposiory insiuions were given he opion o borrow from he Federal Reserve discoun window a an ineres rae ha was fixed o a level above he prevailing federal funds arge rae during a period ha covered he cenury dae change. In SLF, deposiory insiuions were given call opions for credi on July 20, The srike of he opion was se a 150 basis poins above he prevailing federal funds arge rae, and i could be exercised during he period from Ocober 1, 1999, o April 7, These opions were graned free of cos. The second iniiaive was he Sandby Financing Faciliy (SFF), in which he Fed conduced a series of aucions o sell opions conracs. These opions gave he holders he righ, bu no he obligaion, o execue overnigh repo ransacions wih he Federal Reserve Bank of New York a a prese srike price, which was a financing rae ha was 150 basis poins above he prevailing federal funds arge rae. The uni of he opion conrac was $50 million. These opions could be exercised during some specified periods around Y2K. Under SFF, demanders of fuure liquidiy were invied o bid for he opions a periodic inervals before Y2K. The Fed s purpose in issuing hese opions was o insure ha he bond markes operaed smoohly around Y2K so ha he Fed could conduc is moneary policy operaions wihou running ino difficulies. In is Augus 24, 1999, meeing, he FOMC made he necessary rulings o permi he aucion of hese opions. 4 In SFF, opions were sold in uniform-price aucions, which is he curren form of aucions for he issuance of all Treasury deb securiies. The supply in each aucion is he oal amoun acceped in he aucion. This amoun is announced before each aucion. However, he resul of an aucion probably affeced he amoun he Fed planned o accep in he nex aucion. The Fed increased he quaniies in he second and he hird aucions because he demand in he firs round surpassed he Fed s expecaions. The price deermined by he supply and demand in an aucion is referred o as he sop-ou rae. 5 The sop-ou rae conains useful informaion abou he liquidiy demand since he bidders bid afer he supply is announced by he cenral bank. For a fixed supply, he higher he sop-ou rae he bidder is willing o pay for buying he opion on liquidiy, he greaer he demand for he public provision of privae liquidiy. The Federal Reserve Bank of New York conduced seven aucions in SFF, selling hree ypes of opions wih varying mauriy daes in each aucion. The aucions were on he following seven daes in 1999: Ocober 20, Ocober 27, November 3, November 10, November 17, November 23, and December 1. The firs ype of opions allowed he holder o exercise during he period from December 30, 1999, o January 5, 2000, which covered he Millennium Dae Change. This opion is referred o as he December 30 srip by he Fed. The second allowed he holder o exercise during he period from December 23, Downloaded from hp://rfs.oxfordjournals.org a Columbia Universiy Libraries on Augus 3, Source: Press release by he Federal Reserve Bank of New York on Sepember 8, Sop-ou raes are quoed in basis poins. Ten basis poins for an opion on $50 million overnigh loan are equivalen o $138.89, which is calculaed from $50,000,000 (10/360) (1/100) (1/100). 1027

8 The Review of Financial Sudies / v 22 n Table 1 Basic characerisics of he aucions of Y2K opions Aucions Oc 20 Oc 27 Nov 03 Nov 10 Nov 17 Nov 23 Dec 01 December 30 srip Toal amoun of bids Acceped amoun Raio of acceped o oal Sop-ou rae (basis poin) January 6 srip Toal amoun of bids Acceped amoun Raio of acceped o oal Sop-ou rae (basis poin) December 23 srip Toal amoun of bids Acceped amoun Raio of acceped o oal Sop-ou rae (basis poin) The quaniy of bids and he acceped amouns are repored in billions of dollars. The sop-ou raes are quoed in basis poins. The raio of acceped o oal is he oal amoun of bids divided by he acceped amouns. 1999, o December 29, The hird allowed he holder o exercise during he period from January 6, 2000, o January 12, The las wo opions are referred o as he December 23 srip and he January 6 srip, respecively. Through he opion conracs in SFF and SLF, he cenral bank assured he availabiliy of a large amoun of liquidiy around Y2K. Using SFF, he Fed sold a large quaniy of liquidiy insurance o Treasury bond dealers. Table 1 presens a summary of he opions issued in SFF. The oal repo conracs sold in he opions of he December 30 srip were worh $223 billion. The oal repo conracs sold in he opions of December 23 and January 6 srips were worh $114 billion and $144 billion, respecively. To ge a perspecive on he significance of hese opions, we noe ha he average ousanding repo in 1999 was $1361 billion; his implies ha he December 30 srip was abou 16% of he average daily ousanding repo. In addiion, he Fed commied iself, hrough SLF, o providing deposiory insiuions wih an alernaive source of liquidiy for handling poenially large wihdrawals (demand for liquidiy) of deposis or currencies. This commimen shaped he expecaions abou he availabiliy of year-end liquidiy. 6 The opions issued in SFF are disinc from hose in SLF in several ways. Firs, he holders of opions operaed in differen markes; he opion holders in SLF were deposiory insiuions while he opion holders in SFF were bond dealers. One reason for SFF is ha he Fed did no hink he benefis of SLF would be sufficienly ransmied o he bond dealer marke. Second, opions in Downloaded from hp://rfs.oxfordjournals.org a Columbia Universiy Libraries on Augus 3, The Fed repored ha here were 14 insances in which deposiary insiuions borrowed from he Special Liquidiy Faciliy for more han en consecuive days, and anoher 42 insances of borrowing for wo o en consecuive days. This evidence is consisen wih he view ha some financial insiuions did no have inexpensive access o marke sources of funds. (Source: Revisions o Discoun Window Programs, Board of Governors of he Federal Reserve Sysem, Ocober 24, 2002.) 1028

9 Y2K Opions and Liquidiy Premium Table 2 Saisics of he repo raes Repo rae Repo-arge spread A. Sample saisics of repo and repo-arge spread Number of observaions Maximum Minimum Mean Sandard deviaion saisics B. Maximum likelihood esimaes of parameers Parameer a b c d Esimae Sandard error z-value p-value C. Saisics of he subsample of repo-arge spreads Wihin-quarer sample Quarer-end sample Number of observaions Maximum Minimum Mean Sandard deviaion Raio of quarer-end SD o wihin-quarer SD 2.03 The general collaeral raes (repo raes) for overnigh loans are repored in percenage poins. The repo-arge spread is he difference beween he repo rae and he prevailing Fed funds arge rae, which is repored in basis poins. The sample covers he period from May 21, 1991, o Ocober 19, 1999, and is sample saisics are repored in Panel A. The maximum likelihood esimaes of he parameers in Equaion (1) are repored in Panel B. The sample of repo-arge spreads is spli ino wo subsamples: he wihin-quarer sample and he quarer-end sample. The quarer-end sample consiss of he observaions on quarer-end dae and wo business days around i. The res of he observaions belong o he wihin-quarer sample. Panel C presens he saisics of he subsamples, including he mean and sandard deviaion implied by he maximum likelihood esimaes in Panel B. SLF were issued free of cos while opions in SFF were sold for a price. The price-and-demand curves of he opions in SFF allow us o examine he marke view of he liquidiy shorage prior o Y2K, while such an examinaion is no possible wih he free opions in SLF. In he res of his paper, we refer o he opions in SFF as Y2K opions. 2. Price-and-Demand Funcions of Y2K Opions 2.1 Repo as he underlying In order o undersand he payoff and value of Y2K opions, we firs examine he behavior of he general collaeral repo rae. The repo rae is he underlying rae of Y2K opions because dealers mus collaeralize heir overnigh borrowing from he Fed. In Panel A of Table 2, we presen he summary saisics of repo raes from May 21, 1991, o Ocober 19, The beginning dae is he firs Downloaded from hp://rfs.oxfordjournals.org a Columbia Universiy Libraries on Augus 3,

10 The Review of Financial Sudies / v 22 n Figure 3 Behavior of repo raes For he period from May 21, 1991, o January 31, 2000, he general collaeral raes (repo raes) for overnigh loans are ploed along wih he Fed funds arge raes raised by 150 basis poins. A doed verical line indicaes he firs day of a quarer. A solid verical line indicaes he firs day of a year. dae of our daa, 7 and he las dae is he day before he firs aucion of Y2K opions. Since he srike prices of Y2K opions are quoed as he spread over he prevailing Fed funds arge rae, in Panel A of Table 2, we also provide he saisics for he spread beween he repo rae and he arge rae during he same period. The repo rae ends o spike a quarer-ends (including year-ends). In Figure 3, we plo he repo raes over he period. Along wih he repo raes, we plo he Fed funds arge raes afer adding 150 basis poins. As one migh expec, on mos days he repo rae is very close o (in fac, slighly below) he Fed funds arge rae. Neverheless, he repo rae ofen spikes, and he spikes end o occur one or wo days before he quarer-ends and year-ends. Undersanding hese spikes is essenial for he valuaion of Y2K opions because he mauriy of he December 30 srip of Y2K opions spanned over a year-end bu he mauriy daes of he oher wo srips did no. The lieraure has documened ha shor-erm ineres raes end o rise near quarer-ends or year-ends. For example, using one-monh LIBOR and relaed derivaives, Griffihs and Winers (2005) and Neely and Winers (2005) have Downloaded from hp://rfs.oxfordjournals.org a Columbia Universiy Libraries on Augus 3, We obained he repo and Fed funds raes from Bloomberg. The earlies dae of hese daa available from Bloomberg is May 21,

11 Y2K Opions and Liquidiy Premium shown ha shor-erm ineres raes end o rise a year-ends. Such a rise is aribued o increases in risk or preference for cash around quarer-ends or year-ends. Muso (1997) noes ha commercial paper ends o sell a a discoun if i maures in he nex calendar year, and aribues he discoun o agency problems. I is well known ha financial insiuions ypically clean up liabiliies in heir accouns for quarer-end or year-end reporing. This is referred o as window dressing, which reduces liquidiy in money markes. Due o window dressing, he volailiy of repo raes wihin a quarer should be differen from he volailiy around a quarer-end (and year-end). We can esimae and es he difference beween he repo rae s behavior around a quarer-end and is behavior wihin a quarer. We examine he subsample of he repo-arge spreads ha are on quarer-end daes and wo business days around. For convenience, we refer o his subsample as he quarer-end sample. All he spreads ha are more han wo days away from quarer-end daes consiue anoher sample, which is referred o as he wihin-quarer sample. To es for he difference beween he wo subsamples, we use he maximum likelihood mehod o esimae he following specificaion: r = a + bi + ε, ε N(0, exp(d + ci )), (1) where r is he repo-arge spread, and I is he dummy variable ha equals 1 when is in he quarer-end sample and 0 oherwise. We chose model (1) because i is a sandard and convenien approach o esimaion and es of muliplicaive heeroskedasiciy, which is exacly he problem we have here. The model preserves he resricion ha variance is posiive bu allows for simple maximum likelihood esimaion and ess for heeroskedasiciy, which is a problem for a simple linear regression. The properies and advanages of his model are discussed exensively by Harvey (1976). The model is also discussed in inroducory exbooks like Greene (1997) and Judge, Hill, Griffihs, and Lee (1985). 8 The mean and volailiy of he repo rae around a quarer-end are significanly differen from hose wihin a quarer. We can see he difference by examining he esimaes of he parameers a, b, c, and d, which are repored in Panel B of Table 2. All of hese esimaes are significanly differen from zero. The mean and sandard deviaion of he subsamples implied by hese parameers are repored in Panel C. Parameer a = 1.61 is he average repo-arge spread of he wihin-quarer sample. Parameer b = is he difference beween he means of he wo subsamples, indicaing ha he quarer-end sample has a much higher mean han he wihin-quarer sample. Parameer d = 5.47 implies ha he sandard deviaion of he wihin-quarer sample is e d/2 = Parameer c = 1.42 indicaes ha he raio of he quarer-end sandard deviaion o he wihin-quarer sandard deviaion is e c/2 = The significance of b and Downloaded from hp://rfs.oxfordjournals.org a Columbia Universiy Libraries on Augus 3, I is so widely used ha he economerics package STATA has a command ha gives all he resuls abou he model afer simply feeding in he daa. 1031

12 The Review of Financial Sudies / v 22 n Figure 4 Spread beween repo raes and Fed funds arge raes For four monhs around Y2K, he spread beween repo raes and Fed funds arge raes are ploed along wih is hree-day moving average. A doed verical line indicaes he firs day of a quarer. c in model (1) is consisen wih he empirical evidence of window dressing repored in he lieraure. Since repo conracs are collaeralized loans and Fed funds are no collaeralized, repo raes should normally be lower han Fed funds raes bu no around quarer-ends. In he wihin-quarer sample, he repo raes are on average lower han he arge raes by 1.61 basis poins (bps) and saisically significan (Panel C of Table 2). This number is consisen wih he inuiion ha collaeral should reduce he ineres rae on a loan. However, his inuiion does no hold for he quarer-end sample. Ineresingly, his inuiion does no hold in he complee sample eiher (Panel A of Table 2); he mean of he spread beween repo and arge raes is far smaller han one basis poin (only 0.25 bps), and he -saisic is insignifican (only 0.65) for es of zero mean. The jump in he repo-arge spread around Y2K is no maerially differen from oher jumps around quarer- or year-ends. In Figure 4, we plo he spread beween he repo rae and Fed funds arge rae over he las hree monhs of 1999 and he firs monh of The spread has a ypical spike as hose on oher quarer-ends or year-ends. A special feaure is he big drop of he repo rae before New Year s Day. The Federal Reserve Bank of New York used morning repo raes o char he behavior of repo raes on he days around Y2K; 9 we reprin he char in Figure 5 for ready reference. The repo raes in he figure fell significanly in he las few days before Y2K. The Fed s annual repor suggess ha he drop is due o he Fed s provision of liquidiy righ before Y2K. Noice Downloaded from hp://rfs.oxfordjournals.org a Columbia Universiy Libraries on Augus 3, Domesic Open Marke Operaions during 1999, he Federal Reserve Bank of New York, Markes Group, February

13 Y2K Opions and Liquidiy Premium Figure 5 Repo raes around Y2K repored by he Fed Reprin of Char 21 in Domesic Open Marke Operaions during 1999 by he Federal Reserve Bank of New York. The char displays he average of morning levels of Treasury repo raes, morgage-backed securiy repo raes, and Fed fund raes around year-end. ha our moving average of repo-arge spreads in Figure 4 is consisen wih he char in Figure Premium of Y2K opions An imporan quesion is wheher he observed prices of Y2K opions conained any premium, which is aribuable o a poenial jump in repo raes a he end of I is clear ha he price of he December 23 srip should have conained lile year-end or Y2K premium because i maured well before he end of If here was a year-end premium and/or a Y2K premium, i is mos likely o be refleced in he price of he December 30 srip, as i could be exercised in he week ha covered Y2K. The January 6 srip migh also conain some Y2K premium if he marke expeced he Y2K problem o las beyond he firs few days of As shown in Table 1, he sop-ou rae of Downloaded from hp://rfs.oxfordjournals.org a Columbia Universiy Libraries on Augus 3,

14 The Review of Financial Sudies / v 22 n he December 30 srip is much higher han he sop-ou raes of hese oher wo srips. The high sop-ou rae of he December 30 srip alone is no sufficien for us o conclude ha a Y2K premium exised in he price of Y2K opions. Firs, hese opions had differen mauriies. Second, he opions were aucioned on differen daes and consequenly have differen levels of underlying repo raes on hose daes. Third, and mos imporanly, given he fac ha repo raes usually have higher volailiy around a quarer-end (or a year-end) han during a quarer, he December 30 srip of Y2K opions was expeced o be more expensive han he oher wo srips, even if here was no concern abou he Y2K problem a he end of We wish o know wheher here was an incremenal premium due o he effec of Y2K. Unforunaely, here are no repo opions around oher year-ends for us o compare wih Y2K opions. The value of Y2K opions should, however, be very low if he marke did no believe ha an unusual jump on Y2K is likely. Based on he hisorical behavior of he repo rae up o he las quarer of 1999, Y2K opions should no have been expeced o be in he money if Y2K were no expeced o affec he overnigh borrowing rae. Since he payoff of a Y2K opion is a linear funcion of he repo-arge spread if he opion is in he money (i.e., if he repo rae is above he Fed funds arge rae by more han 150 bps) and he payoff is zero oherwise, he value of a Y2K opion depends on he likelihood ha he repo-arge spread is above 150 bps. The saisics in Table 2 show ha he maximum repo-arge spread in our sample is 145 bps and is dae is December 30, 1996, which is a year-end. Therefore, if repo raes are no expeced o jump over he hisorical maximum level of 145 bps, i is very unlikely for he Y2K opions o be in he money. As a maer of fac, he Y2K opions were never exercised by he buyers. Apparenly, he Fed se he srike price high enough ha hese opions were used as insurance for Y2K shocks bu no for he ypical year-end jumps of shor-erm raes. To compare he prices of Y2K opions, we need a valuaion framework. In order o use he sandard opions pricing framework, we need o make he following addiional assumpions. Firs, we assume ha he marke had perfec foresigh abou he acions aken by he FOMC. This allows us o absrac from he fac ha he srike prices were sochasic. In addiion, we need o absrac from he fac ha no secondary marke exised for hese opions. Under hese assumpions, Y2K opions are caples on he repo rae. We use Black s model of ineres rae caps o calculae heir implied volailiies so ha we can compare values of opions on he same underlying bu wih differen imes o mauriy and differen srike prices. Srike rae K is 150 basis poins above he arge rae. The size of he loan, denoed by L, in one Y2K opion conrac can be viewed as $50 million because i is he incremen of he bids. The expiraion ime of he opion is he expiraion period of a srip, which is of Bermudan-ype and conains a few days. In order o use Black s formula, we rea Y2K opions as European opions ha maure only on a paricular day in he expiraion period Downloaded from hp://rfs.oxfordjournals.org a Columbia Universiy Libraries on Augus 3,

15 Y2K Opions and Liquidiy Premium and denoe he dae by T. 10 The iming of he caple s payoff is a day afer he exercise of a Y2K opion and is denoed by T. I is imporan o poin ou ha Y2K opions differ from he exchangeraded opions in several respecs. Firs, he srike price was linked o he arge Fed funds rae a he ime he opions were exercised. This implies ha he srike price was poenially sochasic o he exen ha here was significan uncerainy abou he acions of he FOMC. Second, he arge Fed funds rae is no a marke-deermined ineres rae or he yield on a raded asse. This implies ha he convenional approach o valuing opions (using he equivalen maringale measure) is no valid for deermining he value of hese opions. Third, hese opions did no have a secondary marke and as such are more like execuive sock opions. The valuaion of such opions requires he explici modeling of preferences of invesors. For hese reasons, an applicaion of sandard opions pricing models should be viewed as an approximaion. Wih he parameers specified earlier, Black s formula (see Chaper 20 of Hull, 2000) for he value of a caple is c = e rt L(T T )[FN(d 1 ) KN(d 2 )], (2) d 1 = ln(f/k ) + 0.5σ2 T σ, (3) T d 2 = d 1 σ T, (4) where N( ) is he cumulaive disribuion funcion of he sandard normal disribuion. Besides hose parameers specified in a caple conrac, he formula needs hree variables, which are deermined by he capial markes. The firs is r, which is he yield o mauriy for a zero-coupon bond ha maures a T and can be obained from he erm srucure of LIBOR conracs. The second is F, which is he forward repo rae for he period from T o T and can be obained from he curve of erm repo raes. The hird is c, which is he price of he opion and can be calculaed from he sop-ou rae (please refer o Foonoe 5 for he ransformaion from sop-ou raes o dollar values). Now, he only unobservable parameer in he formula is he volailiy σ of he underlying. Solving for σ from Equaions (2), (3), and (4) gives he implied volailiy of Y2K opions, which are repored in Table 3. A graphical presenaion of he implied volailiies is shown in Figure 6. The implied volailiies sugges ha he dealers fel ha large jumps in repo raes migh happen during a narrow period surrounding January 1, Judged by implied volailiy, he December 30 srip is considerably more expensive han he December 23 srip. The raios presened in Table 3 indicae ha he implied volailiy of he December 30 srip is wice as big as he implied volailiy of he December 23 srip in mos aucions. Clearly, he price of he December 30 Downloaded from hp://rfs.oxfordjournals.org a Columbia Universiy Libraries on Augus 3, In fac, changing he choice of he mauriy dae in he expiraion period of Y2K opions causes only negligible changes in our resuls. 1035

16 The Review of Financial Sudies / v 22 n Table 3 Implied volailiies of Y2K opions Aucions Oc 20 Oc 27 Nov 03 Nov 10 Nov 17 Nov 23 Dec 01 Implied volailiies Dec 30 Srip Jan 6 Srip Dec 23 Srip Volailiy raios Dec 30/Dec Jan 6/Dec Dec 30/Jan Based on he sop-ou raes of Y2K opions, implied volailiies are calculaed from Black s formula of ineres rae caps. The volailiies are repored in percenage poins. A volailiy raio is he implied volailiies of a srip divided by he implied volailiy of anoher srip. Figure 6 Implied volailiy of Y2K opions Based on he sop-ou raes of Y2K opions, implied volailiies are calculaed from Black s formula for ineres rae caps. The implied volailiy of each srip of Y2K opions is ploed over he seven aucion daes. srip conains a leas a premium on he year-end jump of borrowing rae. Given he fac ha he srike price of Y2K opions was se so high ha he opions would no be in he money wih he maximum hisorical repo-arge spread, we suspec ha a leas par of he opion s premium refleced concerns abou he Y2K shocks beyond he usual year-end jumps. Ineresingly, he implied volailiy of he January 6 srip is abou he same as (and even slighly smaller Downloaded from hp://rfs.oxfordjournals.org a Columbia Universiy Libraries on Augus 3,

17 Y2K Opions and Liquidiy Premium han) he implied volailiy of he December 23 srip, indicaing ha nohing unusual in he week afer Cenury Dae Change was expeced. In order o see wheher a premium due o a jump beyond he usual year-end effec exiss in he December 30 srip of Y2K opions, we compare he implied volailiies wih he sandard deviaion of he repo-arge spread. The Y2K opions in he December 23 srip should be a funcion of he volailiy during a quarer, while he opions in he December 30 srip should be a funcion of he volailiy a quarer-end. For he repo-arge spread, he raio of he sandard deviaion of he quarer-end sample o he sandard deviaion of wihin-quarer sample is 2.03 (Panel C of Table 2). If Y2K is no an incremenal shock o he usual year-end effec, hen he raio of he implied volailiies for he wo srips should be comparable wih he raio of he sandard deviaions in he wo subsamples of repo-arge spreads. In conras, he raio of he implied volailiy of he December 30 srip o he implied volailiy of he December 23 srip is abou 2.50 in hree aucions and above 2.03 in all excep he las wo aucions (Table 3). We view his as an indicaion of he Y2K premium in he December 30 srip. In he las aucion, he raio of implied volailiies of he wo srips is only If we ake he sand ha 2.03 is a normal level for he raio of quarer-end volailiy o wihin-quarer volailiy, he low raio in he las aucion indicaes ha he marke expeced a shock even smaller han he usual year-end. The implied volailiies indicae ha dealers expecaion of a year-end jump changed over he seven aucions. For he purpose of our analysis in laer secions, he relevan issue is no wheher here is a Y2K premium in addiion o he usual year-end premium. Raher, he key issue is wheher he Fed s acions influenced he funding coss of dealers. In his conex, he variaion, raher han he level, of he implied volailiies over he aucions is imporan; he variaion poins o he effec of he cenral bank s commimen of funds and he change of views by marke players. In Table 3, and more visibly in Figure 6, he implied volailiy of he December 23 srip remains almos consan. This indicaes ha he dealer s view of he wihin-quarer repo raes was no changing or influenced by he issuance of Y2K opions. The implied volailiy of he December 30 srip, however, varied over he aucions. Then, he raio of he implied volailiy of he December 30 srip o he implied volailiy of he December 23 srip varied accordingly. In conras, he implied volailiy of he January 6 srip did no vary as much over he aucions. I is necessary o undersand wheher he change in he implied volailiies of Y2K opions is caused by he change in he expecaion of he repo rae volailiy shorly afer he cenury dae change. This would have been difficul o address, if he Y2K opions issued by he Fed had consised of only one srip wih a fixed mauriy period. Forunaely, he Y2K opions aucioned o he dealers include a srip of mauriy before he cenury dae change and a srip of mauriy afer he cenury dae change. If he change in he implied volailiies of Y2K opions is caused by he change in he expecaion of he Downloaded from hp://rfs.oxfordjournals.org a Columbia Universiy Libraries on Augus 3,

18 The Review of Financial Sudies / v 22 n repo rae volailiy shorly afer he cenury dae change, he implied volailiies of he December 23 srip should be differen from he implied volailiies of he January 6 srip. However, Figure 6 shows ha he implied volailiies are he same for he wo srips. In conras, he implied volailiies of he December 30 srip are much higher han he implied volailiies of he oher srips. This means ha a large par of he increase in he implied volailiy of a December 30 srip is he premium on he volailiy in he daes of he cenury dae change. Furhermore, afer hree aucions, he implied volailiies of he December 30 srip dropped significanly, while he implied volailiies of he oher srips did no. This is inconsisen wih he hypohesis ha he general level of he repo rae uncerainy was expeced o be higher. 2.3 Aggressiveness of demand Since he evidence repored in he previous secion based on Black s model is only an approximaion, in his secion we provide addiional evidence ha is based direcly on he aggressiveness of he bids in he aucions. The evidence in his secion does no rely on he assumpions ha we made for he applicaion of Black s model. The variaion of he demand for Y2K opions over he seven aucions should reflec he effecs of he Fed s acion on marke condiions. Wih he Fed s inenion o ensure ha dealers have enough proecion agains shocks so ha hey do no wihdraw from he marke, he Fed adjused he fuure acceped amoun afer each aucion o saisfy he oal demand for liquidiy proecion. In each aucion, he acceped amoun (supply) should direcly affec he implied volailiy of Y2K opions in he aucion. I migh also indirecly affec he implied volailiy in he laer aucions if i affeced he demand funcions in laer aucions. According o is 1999 repor of open marke operaions, he Federal Reserve Bank of New York believes ha he demand was saisfied, ciing he drop of he price and demand in he las aucion. Wih he daa obained from he Federal Reserve Bank of New York, we can esimae he demand funcions in each aucion. We use he sandard demand funcion wih consan elasiciy. The funcional form is Q = e a P b, (5) where Q is he quaniy of he Y2K opions quoed in billions of dollars of repurchase agreemens and P is he price of he Y2K opions quoed in basis poins. We esimae he parameers a and b from he regression ln(q i ) = a b ln(p i ) + ε i, (6) where Q i is he oal quaniy of bid a prices lower han or equal o price P i.the parameer a is he inercep of he loglinear regression of he demand funcion. The parameer b is he demand elasiciy, which measures he sensiiviy of quaniy o price changes. The assumpion of consan elasiciy is moivaed no only by simpliciy bu also by he fac ha we have a problem wih small Downloaded from hp://rfs.oxfordjournals.org a Columbia Universiy Libraries on Augus 3,

19 Y2K Opions and Liquidiy Premium Figure 7 The demand curves in he aucions of Y2K opions Demand and supply in aucions of he December 30 srip of Y2K opions. The acceped amoun (supply) is indicaed by he verical line ha mees he demand curve, and a horizonal line indicaes he price (sop-ou rae). sample size. The relaively small number of grids of bidding price and quaniy 11 renders he esimaion of a more general demand curve difficul. For he December 30 srip, we plo he esimaed demand curves in he seven aucions (Figure 7). The acceped amoun (supply) is indicaed by he verical line ha mees he demand curve, and he horizonal line indicaes he sop-ou Downloaded from hp://rfs.oxfordjournals.org a Columbia Universiy Libraries on Augus 3, In SFF, he incremen in price is 0.5 basis poins and he incremen in quaniy is $50 million. 1039

20 The Review of Financial Sudies / v 22 n Table 4 Aggressiveness of demand for Y2K opions Aucions Oc 20 Oc 27 Nov 03 Nov 10 Nov 17 Nov 23 Dec 01 December 30 srip Elasiciy of demand Inercep in regression Aggressiveness January 6 srip Elasiciy of demand Inercep in regression Aggressiveness December 23 srip Elasiciy of demand Inercep in regression Aggressiveness Aggressiveness raios Dec 30 srip/dec 23 srip Jan 6 srip/dec 23 srip Dec 30 srip/jan 6 srip A demand funcion is esimaed by a regression of log quaniy on log sop-ou rae. The elasiciy of demand is he slope coefficien in he regression. The aggressiveness of demand is he value of e o he power of he inercep. The aggressiveness raio is he aggressiveness for a srip divided by he aggressiveness for anoher srip. rae. We presen he demand and supply only for he December 30 srip because his srip conains he premium for year-end and Y2K, as we have demonsraed previously. We wan o know how aggressively dealers bid in each aucion. For his purpose, we can compare he quaniy demanded in one aucion a a price wih he quaniy demanded in anoher aucion a he same price. Le a and a be he inerceps in he loglinear regressions of wo demand funcions. If he wo demand funcions have he same elasiciy, hen he raio of he wo quaniies demanded a any price level is e a a. In his sense, e a measures he aggressiveness of he demand because he quaniy demanded for any given price is an increasing funcion of a. If wo demand funcions have differen elasiciy, e a a is he raio of he quaniies demanded a price P = 1. Therefore, e a is he quaniy demanded a uni price. We hus refer o e a as he aggressiveness of he demand. In Table 4, we provide he demand aggressiveness and elasiciy for each aucion of each srip of Y2K opions. The aggressiveness of demand shows ha dealers were concerned abou a poenial shock on he Y2K dae, bu no before or afer i. This can be seen clearly in Figure 8. On each aucion dae, he demand for he December 30 srip is always more aggressive han he demand for he oher wo srips. I suggess ha he year-end or Y2K concerns brough abou srong demand for he December 30 srip. In conras, he aggressiveness of he demand for he January 6 srip is only slighly higher han he December 23 srip. Dealers did no seem o worry abou prolonged problems afer Y2K. To look a he relaive Downloaded from hp://rfs.oxfordjournals.org a Columbia Universiy Libraries on Augus 3,

21 Y2K Opions and Liquidiy Premium Figure 8 Aggressiveness of demand for Y2K opions A demand funcion is esimaed by a regression of log quaniy on log sop-ou rae. The aggressiveness of a demand is he value of e o he power of he inercep of he regression. The aggressiveness of demand for each srip of Y2K opions is ploed over he seven aucion daes. aggressiveness, we repor, in Table 4, he raio of he aggressiveness for he December 30 srip o he aggressiveness for he December 23 srip. This raio varies drasically over he seven aucions and has a downward rend. Indeed, dealers bid aggressively for he insurance of Y2K shock in early aucions bu much less so in laer aucions. The aggressiveness of he demand for he December 30 srip was high on Ocober 27 and November 3. I sared o diminish in he aucion on November 10. The demand curves for he las hree aucion daes, ploed in Figure 7, clearly show a significan drop. In he las aucion, he aggressiveness of he demand for he December 30 srip was abou he same as he demand for he oher srips. The variaion of he aggressiveness for he December 23 or he January 6 srip was much smaller han he variaion for he December 30 srip. Therefore, he Fed s acion exered a large influence on he demand for he December 30 srip bu a small influence on he demand for he December 23 and January 6 srips. I is imporan o poin ou ha he aggressiveness measures he bidding behavior a a single aucion independenly. I does no rea he bidding behavior as par of a broader bidding sraegy ha akes ino accoun he knowledge ha here are fuure aucions. Unforunaely, due o confidenialiy issues, he aucion daa provided by he Fed do no allow us o rack individual bidders for sraegic bidding behavior. To complicae maers, he Fed was also learning from each aucion and dynamically alering he supply. Is he drop of price and demand of Y2K opion relaed o he drop in liquidiy premium? The Federal Reserve Bank of New York believes ha he price of Y2K opions conains a liquidiy premium and he demand of Y2K opions Downloaded from hp://rfs.oxfordjournals.org a Columbia Universiy Libraries on Augus 3,