Extracting the Expected Path of Monetary Policy from Futures Rates * Brian Sack

Transcription

1 Exracing he Expec Pah of Moneary Policy from Fuures Raes * Brian Sack Division of Moneary Aairs Board of Governors of he Feral Reserve Sysem Washingon, DC Sepember 17, 2002 * The opinions express are hose of he auhor and do no necessarily reflec he views of he Board of Governors or oher members of is sa. I hank Jim Clouse, Lou Crandall, Benson Durham, Bill English, and Refe Gürkaynak for helpful commens. Correspondence can be direc o he above address, or o bsack@frb.gov. 1

2 Exracing he Expec Pah of Moneary Policy from Fuures Raes Absrac Feral funds and eurodollar fuures conracs are among he mos useful insrumens for deriving expecaions of he fuure pah of moneary policy. However, reading policy expecaions from hose insrumens is complica by he presence of risk premia. This paper demonsraes how o exrac he expec policy pah under he assumpion ha risk premia are consan over ime, and under a simple model ha allows risk premia o vary. In he laer case, he risk premia are idenifi under he assumpion ha policy expecaions level ou afer a long enough horizon. The resuls provide evidence ha he risk premia on hese fuures conracs vary over ime. The impac of his variaion is fairly limi for fuures conracs wih shor horizons, bu i increases as he horizon of he conracs lenghens. 2

3 Inroducion Feral funds and eurodollar fuures conracs are among he mos useful insrumens available for deriving expecaions abou he pah of moneary policy. These markes have impressive liquidiy for conracs ha span a range of horizons, and he values of he conracs are explicily i o realizaions of shor-erm ineres raes. Marke paricipans ofen use hese markes o hge heir exposures o changes in he level of shor-erm ineres raes or simply o ake posiions on he direcion of moneary policy. Inde, marke commenary on he valuaion of hese conracs is domina by opinions abou when he Feral Reserve s nex policy acion migh ake place and is direcion and magniude. Besides being widely us by marke paricipans for hese purposes, academic researchers have also employ hese fuures conracs o measure marke forecass of he feral funds rae. 1 Gürkaynak, Sack, and Swanson (2002) direcly compare he pricive power of hese fuures raes o a number of oher marke-bas measures of policy expecaions. Their resuls indicae ha feral funds fuures dominae oher marke insrumens a forecasing he feral funds rae over horizons ou o several monhs, and ha eurodollar fuures perform marginally beer han many oher insrumens a longer horizons. Thus, he pracice of relying on hese markes for policy expecaions is empirically well suppor. This paper akes an in-deph look a how feral funds and eurodollar fuures raes can be us o exrac he expec fuure pah of moneary policy. The primary 1 Among oher papers, Kruger and Kuner (1996), Carlson, McInire, and Thomson (1995), Roberson and Thornon (1997), and Södersröm (2001) have us feral funds fuures o pric moneary policy decisions, and Rudebusch (2002) and Jegadeesh and Pennacchi (1996) have us eurodollar fuures. Lange, Sack, and Whiesell (2002) presen evidence on he pricive power of boh feral funds and eurodollar fuures conracs. 3

4 challenge in his process is accouning for he risk premia embd in he fuures raes. The analysis ha follows begins by showing how o adjus for risk premia under he assumpion ha hey are consan over ime, as in many applicaions in he lieraure. However, here is no reason o expec his assumpion o hold, and hus he paper urns o an alernaive approach ha allows for some variaion in he risk premia over ime. The approach relies on a simple idenificaion assumpion ha policy expecaions level ou beyond a horizon of several years. Under ha assumpion, dierences beween fuures raes on conracs wih long enough horizons will be driven primarily by heir risk premia. These long-horizon fuures raes can herefore be us o derive a proxy for a facor underlying movemens in he risk premia on all fuures conracs. The resuls provide evidence ha he risk premia on hese fuures conracs do, in fac, vary over ime. The impac of his variaion is fairly limi for conracs wih shor horizons, bu i increases as he horizon of he conracs lenghens. The analysis hen demonsraes ha porfolios of fuures can be consruc o measure policy expecaions ha auomaically accoun for his variaion. The Informaion Conen of Fuures Raes Feral funds and eurodollar fuures raes are direcly influenc by he oulook for shor-erm ineres raes. The value of a feral funds fuures conrac expiring i monhs ahead is explicily i o he average of he eecive overnigh feral funds rae during he calendar monh of expiraion, f f (i), according o he formula 100 ( i). 2 (All raes us here are measur in percenage poins.) The value of a eurodollar fuures 2 The eecive funds rae is conver o a daily series before averaging, so ha observaions on Fridays and before holidays carry addiional weigh. 4

5 conrac wih an expiraion i quarers ahead is insead i o he hree-monh Libor rae realiz on he expiraion dae, lib(i), according o 100 lib( i). Given he abiliy of invesors o subsiue beween a hree-monh eurodollar deposi and a sraegy of rolling over loans in he overnigh feral funds marke, he Libor rae will be srongly influenc by he feral funds rae expec o prevail over he subsequen hree monhs. Neverheless, he linkage beween hose raes is no exac. Thus, i is useful o hink of he paymen on he eurodollar fuures conrac as having wo componens, 100 ( i) lib( i) ( i). The firs erm in his payou is equivalen o ha of feral funds fuures, only where he average of he feral funds rae is aken over a hree-monh period saring a he expiraion of he fuures conrac. 3 The second erm reflecs basis risk, or any dierences ha migh arise beween he Libor rae and he average feral funds rae. The prices of feral funds and eurodollar fuures conracs wih expiraions i periods ahead, P (i) and P (i), respecively, are ofen conver o raes, which I denoe fu (i) and fu (i), according o he formulas P ( i) 100 fu ( i) and P ( i) 100 fu ( i). These fuures raes can be express as he sum of he expec fuure level of he underlying ineres rae and a risk premium, as follows: fu fu ( i) ( ) ( i) E i (1) lib( i) ( ) ( i) E i. (2) 3 Acually, he eurodollar fuures rae prics he hree-monh reurn from rolling over overnigh feral funds loans, and hence he daily feral funds raes should be compound. This compound reurn will approximaely equal he average feral funds rae over he hree-monh period. 5

6 The risk premia, (i) and (i), represen he expec excess reurn o an invesor who is long he fuures conrac, which compensaes he invesor for he uncerainy associa wih he reurn o aking ha posiion. 4 The equaion for eurodollar fuures mus be modifi o express he expecaions in erms of he feral funds rae raher han he Libor rae, as follows: where he erm lib (i) fu equals lib( i) ( i) lib ( i) ( i) ( ) ( i) E i, (3) E. Thus, when express in erms of he expec feral funds rae, he eurodollar risk premium has an addiional componen (i) ha equals he excess expec reurn of he hree-monh eurodollar deposi over lib he feral funds rae. This erm will ypically be posiive, reflecing ha invesors face greaer cri risk by lending o an insiuion for a hree-monh period raher han on an overnigh basis. 5 According o (1) and (3), he raes on feral funds and eurodollar fuures can be us as proxies for expecaions of he feral funds rae over dieren horizons, once one appropriaely conrols for he risk premia embd in hose raes. In ha case, by using fuures quoes covering dieren horizons, one could derive he enire pah of he expec feral funds rae. To do so, I will use feral funds fuures wih expiraions ou o four monhs, and eurodollar fuures wih expiraions ou o five years. These markes are excepionally liquid for feral funds fuures expiring over he firs several monhs and for eurodollar fuures expiring over he nex couple years. Eurodollar fuures 4 This paper refers o hese erms as risk premia, bu hey acually encompass any facors resuling in an excess reurn on he conrac, including insiuional deails, hging aciviy, and liquidiy consideraions. Gürkaynak, Sack, and Swanson (2002) oer a more deail discussion of he deerminaion of risk premia. 5 Noe ha here will also be a risk premium rela o his basis risk, which is a componen of he risk premium on he eurodollar fuures conrac, (i). 6

7 wih longer horizons have less aciviy, bu liquidiy remains high enough o use hose insrumens for he purposes explain below. 6 Policy Expecaions under Consan Risk Premia There exiss a large lieraure on he pricive power of marke ineres raes ha imposes he assumpion ha he risk premia embd in hose raes are consan over ime an assumpion ha is ofen referr o as he expecaions hypohesis. Under ha assumpion, he expec pah of he feral funds rae can be obain by subracing an esimae of he risk premia from he quo fuures raes. To arrive a a measure of he risk premia embd in hese fuures conracs, his paper relies on he informaion conain in he average shape of he erm srucure of fuures raes. In doing so, I assume ha expec changes in moneary policy have averag o zero over he sample us, which runs from July 1992 o June This assumpion seems reasonable, given ha he policy insrumen has remain in a relaively narrow range over he sample (making is average monhly change close o zero). Moreover, survey evidence roughly suppors he assumpion. According o a weekly survey perform by Money Marke Services, he expec change in he feral funds rae over he subsequen hree monhs averag 2.63 basis poins over our sample less han one basis poin per monh. 7 6 Much of he rading aciviy in eurodollar fuures conracs expiring beyond he nex couple years is in he form of bundles and packs, which are essenially blocks of conracs wih consecuive expiraion daes. 7 The survey measure us was calcula by splicing ogeher wo daa series: he expec feral funds rae six mainenance periods ahead o July 1997, and he expec feral funds rae wo FOMC meeings ahead since hen. The posiive average expecaion error suggess ha he approach us may slighly oversae he average risk premium on near-erm conracs. 7

8 Under he assumpion of zero average expecaion errors, he average levels of feral funds and eurodollar fuures raes relaive o he average level of he overnigh feral funds rae will reflec he risk premia on hose conracs. 8 Thus, his measure, which is shown in Figure 1 and repor in he firs column of Table 1, is aken o be he esimae of he risk premia us in he analysis ha follows. As can be seen, he risk premia on feral funds fuures are very small. However, hey have an upward slope of a couple of basis poins per monh, indicaing ha invesors wih long posiions ypically require a higher reurn on longer-horizon conracs because of he greaer uncerainy associa wih ineres rae movemens. The risk premia on eurodollar fuures conracs sar from a higher level han hose on feral funds fuures conracs and also increase as he horizon is exend, again likely reflecing he greaer uncerainy associa wih movemens in hree-monh Libor over longer horizons. 9 Under he assumpion ha hese risk premia are ime-invarian, one can derive he expec pah of moneary policy simply by subracing he esima risk premia shown in Figure 1 from observ fuures quoes. Some examples of he resuling pahs for he feral funds rae are shown in Figure 2. In he figure, he rae impli by each conrac is shown a he middle of he period cover by ha conrac. 10 In March 2002, he inend feral funds rae was a 1.75 percen, and marke paricipans anicipa ha he FOMC would begin o gradually ighen moneary policy abou wo quarers ahead, 8 An alernaive approach for gauging he size of he risk premia is o use he average ex-pos reurns on fuures conracs, as in Gürkaynak, Sack, and Swanson (2002). The idea is ha expecaion errors for he feral funds rae will average o zero over a long enough sample, so ha he average ex-pos reurns will simply reflec he risk premia. Boh ha approach and he ex-ane approach us in he curren paper are somewha sensiive o he sample chosen, since he period of ime for which daa are available is no suicienly long o ensure ha expec policy changes or expecaion errors average o zero. 9 These paerns are similar o he ex-pos measures repor in Gürkaynak, Sack, and Swanson (2002). 10 In splicing ogeher he raes impli by feral funds and eurodollar fuures, I firs plo he resuls from he feral funds fuures over he curren and following hree monhs, and hen hose from eurodollar conracs expiring beyond hen. 8

9 wih he feral funds rae expec o reach nearly 5 percen afer several years. As indica by he oher daes shown in Figure 2, he expec policy pah can ake a variey of shapes. In early January 2001, marke paricipans had pric in subsanial easing over he subsequen year, alhough far less han was ulimaely realiz. And in May 1998, i appears ha marke paricipans expec policy o ease slowly over he subsequen wo years. Evidence of Variaion in Risk Premia The previous secion demonsraes ha i is sraighforward o derive he expec pah of moneary policy under he assumpion of consan risk premia. Of course, here is no reason o believe ha he risk premia on hese fuures conracs are consan over ime. Inde, his is likely no he case. In general, i is an empirical quesion as o wheher he variaion in he risk premia is large enough o significanly disor he policy expecaions deriv above. Unforunaely, i has proven diicul o derive useful measures of ime varying risk premia. This secion presens some evidence on he exen o which risk premia vary over ime. The analysis firs focuses on he behavior of he componen lib (i), which again is he premium ha invesors demand o exend he horizon of a loan from overnigh ou o hree monhs. Evidence on he behavior of his componen can be obain from quoes on basis swaps. Under hese insrumens, one pary exchanges paymens i o he hreemonh Libor rae (he rae underlying he eurodollar fuures) in exchange for paymens bas on he average overnigh feral funds rae over he subsequen hree monhs precisely he basis risk involv wih eurodollar fuures in he conex discuss above. 9

10 If basis swaps exis for a single fuure paymen, an invesor could creae a synheic feral funds fuures conrac by going long a eurodollar fuure and receiving Libor agains feral funds in he basis swap. In fac, i can be shown ha he spread on such a basis swap (he amoun add o he feral funds paymen in exchange for he lib Libor paymen) is ( i) ( i) ( i). Thus, a porfolio wih a long posiion in a eurodollar fuure (equaion (3)) combin wih his basis swap has a reurn ha is idenical o he feral funds fuures equaion (1), only where he payou bas on he hree-monh average of he feral funds rae raher han he one-monh average. This paper does no pursue he approach of sysemaically creaing synheic feral funds fuures, given ha he marke for basis swaps is less liquid han ha for fuures and ha mos basis swaps involve a sream of paymens raher han a single paymen. 11 Noneheless, he swap quoes ha are available provide useful informaion abou he behavior of lib (i). As shown in Figure 3, basis swap spreads vary some over ime, wih he spreads increasing noably in he fall of 1998 and again in advance of Y2K. 12 The figure also shows ha he erm srucure of basis swap spreads is relaively fla i ypically has a slope of jus a few basis poins over five years. Thus, in he analysis ha follows, I assume ha his componen of he risk premium changes over ime bu is independen of he horizon of he fuures conrac, or lib ( i) c. The basis swap covering a one-year period has rad a an average spread of 21 basis poins over he sample plo, which I ake as he average size of he componen lib (i). 11 Because mos basis swaps involve a sream of quarerly paymens, heir use for hging he basis risk of an individual fuures conrac is no clear-cu. One could smooh a yield curve hrough he basis swap quoes and consruc basis swap forward raes o conver eurodollar fuures ino feral funds fuures. 12 Over he period leading up o Y2K, aciviy in he basis swap marke was probably very ligh, and he spreads may have been influenc by idiosyncraic facors. 10

11 Given ha he componen lib (i) is relaively fla across dieren conrac horizons, he slope of he erm srucure of fuures raes on any given day mus insead reflec eiher moneary policy expecaions or he oher componens of he risk premium, (i) and (i). Noe ha unlike lib (i), hese oher componens of he risk premia will likely depend on he horizon of he conrac, given ha hey measure compensaion for bearing he risks arising from ineres rae changes over ha horizon. 13 To separae hese risk premia componens from policy expecaions, I rely on a simple idenificaion assumpion ha he expec pah of moneary policy levels ou wihin a horizon of four years. 14 I seems unlikely ha marke paricipans formulae views abou significan changes in he feral funds rae aking place four o five years ahead. By ha ime, he precision of heir oulook is weak enough ha heir bes guess is likely o be ha he feral funds rae would be held seady (a a level ha may shif around over ime). If expecaions for he feral funds rae level ou afer some horizon, dierences in eurodollar fuures raes for conracs expiring beyond ha horizon will be influenc only by risk premia. Hence, he approach pursu in his paper is o derive an esimae of he behavior of hese risk premia componens bas on he raes on fuures conracs wih long horizons. This approach is bes undersood by looking a he erm srucure of eurodollar fuures raes ou o a five-year horizon for a recen dae, shown in Figure 4. The raes on 13 The risks underlying he premia (i) and (i) are slighly dieren, in ha one is bas on uncerainy surrounding movemens in he feral funds rae and he oher on uncerainy abou movemens in he hree-monh Libor rae. (The same poin was rais earlier in foonoe 5.) In he applicaion below, I allow hese conracs o have dieren facor loadings o accoun for his consideraion. 14 Some marke paricipans may use a similar approach. Goldman Sachs (2001) repors using he slope of he eurodollar erm srucure from one o wo years ahead o conrol for variaion in he risk premium. Tha repor also argues ha i migh have been beer a ha ime o conrol for he risk premium using a more general measure of he seepness of he erm srucure, such as he slope from wo o en years ahead. 11

12 near-erm conracs are quie low, reflecing he accommodaive sance of moneary policy a ha ime, and he raes rise considerably for conracs expiring in 2003 and 2004, in par reflecing he view ha shor-erm ineres raes will rise over ha period. Beyond ha horizon, he eurodollar curve coninues o have an upward slope and becomes nearly linear for conracs expiring beyond 2004 (excep for he sligh elevaion in every fourh conrac, which reflecs a year-end premium for conracs expiring each December). I urns ou ha he far end of he eurodollar fuures erm srucure is almos always upward sloping. Obviously, i would be diicul o explain his paern bas on policy expecaions ha is, by perennial expecaions of policy ighening. Insead, I assume ha his slope reflecs he risk premia on hose conracs he basis for he idenificaion approach aken here. Under his inerpreaion, I ake he dierence beween he fuures rae expiring five years ahead and ha expiring four years ahead as a proxy for he facor driving he componens of he risk premium (i) and (i). 15 Figure 5 shows a ime series of his slope facor, which I denoe s, since he early 1990s, where he slope is express on a per-monh basis. As is eviden, he measure demonsraes considerable variaion over ime. I was a is wides in he early 1990s and narrow considerably, on balance, ino In he fall of 1998, i widen sharply before narrowing again (alhough i appear eleva from Y2K concerns), and i hen rose considerably over he pas couple years. Looking across all fuures conracs, I assume ha he componens of he risk premium (i) and (i) are driven by a one-facor model in which hey are linearly 15 By using conracs expiring in he same calendar monh, I avoid any disorions arising from he year-end premium, assuming ha i is he same size in boh years. 12

13 rela o he slope facor from Figure 5. The loadings of each conrac on his facor are deno by, so ha ( i) ( i) s and ( i) ( i) s. Noe ha he loadings are ime invarian bu dier across he individual fuures conracs. Thus, he model assumes ha he risk premia for all fuures conracs adjus over ime proporionally o movemens in he slope facor s. The loadings of he individual conracs are deermin so ha he average level of he slope facor explains he average shape of he erm srucure of fuures raes shown earlier in Figure Of course, he eurodollar fuures curve also embs he oher componen of he risk premia, lib (i), which explains why i begins a a higher level, on average, han he feral funds fuures curve. Thus, one mus firs subrac he average size of he componen lib (i) (21 basis poins) from he eurodollar fuures curve. The facor loadings are hen calcula by dividing he remaining average shape of he fuures curves by he average level of he slope facor s, which imposes ha he average shape of he fuures curve is obain when he slope facor is a is average level. 17 Reflecing he shapes shown in Figure 1, he loadings increase more seeply for conracs wih shorer horizons and hen become quie linear a longer horizons. The loadings on he slope facor are repor in he second column of Table 1. The nex secion explores how o derive he expec pah of moneary policy when he risk premia on he fuures conracs are ime varying. 16 A simpler version of he model assumes ha he risk premium is linear in he ime o expiraion of he conrac. In ha case, he measures deriv below simply adjus for he slope of he erm srucure in deriving policy expecaions. 17 Under his procure, he loading on he conrac expiring five years ahead, ( 5y ), will equal 1 (4y), so ha he dierence in he raes of hose conracs will yield s. 13

14 Porfolios as Proxies for Policy Expecaions The expec pah of moneary policy under ime-varying risk premia can be approxima by consrucing simple porfolios of fuures conracs. 18 Under he srucure of he risk premia assum in he previous secion, he raes on eurodollar fuures conracs wih expiraions of four and five years (deno ( 4y) and ( 5y) ) will be deermin as follows: fu (4y) * c (4 y) s (4) fu (5y) * c (1 (4y)) s, (5) where he feral funds rae is assum o reurn o is equilibrium level * wihin four years he idenificaion assumpion us in he previous secion. In he analysis ha follows, hose wo conracs are us o conrol for he ime variaion in he risk premium in any oher fuures conrac. 19 To see ha, consider as an example he rae on he eurodollar fuures conrac expiring a year ahead, which is deermin as follows: fu ( 1y) s, (6) (1y) c (1y ) where f f ( 1y) is he expec average feral funds rae for he hree monhs beginning a year ahead. By consrucing porfolios of he hree fuures conracs (4) o (6), one can derive measures of policy expecaions from he conrac (6) ha have been cleans of 18 An alernaive approach is o formulae a model ha conains addiional srucure, where he model s parameers (including ime-varying risk premia) could be esima across he enire erm srucure of fuures raes. Such a model could incorporae addiional deails abou he fuures marke, such as he exisence of a year-end premium on December conracs. However, a disadvanage of he model approach is ha i would presumably have o impose more srucure on policy expecaions. 19 One canno solve for all of he unknown variables or parameers ha is, f f, *, c, and s in (4) * hrough (6). In paricular, he longer-erm conracs canno separae ou and c separaely. Thus, mos of he porfolios consruc will measure expecaions relaive o one of hose parameers. 14

15 much of he ime variaion in he risk premium. I consider wo dieren porfolio sraegies. Firs, consider a porfolio ha is long one uni of fu ( 1y), long ( 1y) unis of fu ( 4y), and shor ( 1y) unis of fu ( 5y). The basic idea of his porfolio is ha being long fu ( 4y) and shor fu ( 5y) gives he invesor a ne shor posiion of ( 1y) unis of he facor s, which hges he exposure o ha facor arising from holding fu ( 1y). Inde, bas on equaions (4) o (6), he value of his porfolio is as follows: fu ( 1y) c. (7) (1y ) fu (4y) (1y) fu (1y ) (1y) As you can see, his porfolio herefore provides a reading of he expec feral funds rae ha is immune o changes in he slope of he risk premia s, alhough i sill includes he basis erm c. Of course, oher fuures raes can be us o derive similar measures of expecaions a oher horizons. The second porfolio sraegy consider involves long posiions of one uni of fu ( 1y) and ( (4y)- (1y)) unis of fu ( 5y), and a shor posiion of (1+ (4y)- (1y)) unis of fu ( 4y). The value of his porfolio is as follows: fu 1 (4y) (1y ) fu (4y) (4y) (1y) fu (5 ) ( 1y) y. (8) * ( 1y) As can be seen, his porfolio provides a reading of he expec deviaion of he feral funds rae from is long-run level, or a measure of he sance of moneary policy. Noe 15

16 ha his measure is immune o shifs in all componens of he risk premium boh he basis erm c and he slope erm s. For feral funds fuures, he informaion ha resuls from hese measures is slighly dieren, given ha he fuures rae does no conain he risk premium componen c. The rae on a feral funds fuures conrac expiring hree monhs ahead, for example, is given by fu ( 3m) (3m) (3m) s, (9) in which case he payou from porfolio sraegy (7) becomes jus f f ( 3m), and ha from sraegy (8) becomes * ( 3m) c. Thus, he disorion presen by c shifs from one measure o he oher. The ime series of measure (7) is shown for several horizons in Figure 6. In his figure and he ones ha follow, I subrac he average level of c (21 basis poins) from he measure. 20 The measure seems o correspond well wih policy expecaions, generally moving in advance of changes in he arge feral funds rae. Moreover, expecaions wo years ahead ofen move by more han he year-ahead measure, in many cases reflecing expecaions ha he feral funds rae will coninue o move in he same direcion. The impac of variaion in he risk premia on he measuremen of policy expecaions can be sizable. Figure 7 repeas he policy expecaions for wo of he daes shown earlier in Figure 2, bu now showing he esimae under he ime-varying risk 20 As discuss earlier, one could arrive a a ime-varying esimae of c bas on basis swaps. Alernaively, one could esimae i from he dierence beween he spo Libor rae and a combinaion of feral funds fuures expiring over he subsequen hree monhs. 16

17 premia as well. For he March 2002 observaion, he dierence in he pahs is minimal, as he measur risk premium facor ha day was only slighly above he average over he whole sample. The dierence is more subsanial in May 1998, when he risk premium facor was well below is average level over he sample (see Figure 5). Under he assumpion ha he risk premium is consan, one would subrac o oo large of a risk premium, resuling in an expec policy pah wih more han a percenage poin of easing over he subsequen hree years. The smaller adjusmen made under he imevarying risk premium model insead resuls in policy expecaions ha are largely fla, consisen wih marke commenary a ha ime. 21 The second measure of policy expecaions, equaion (8), is shown in Figure 8. This measure appears o provide a plausible proxy for he expec sance of moneary policy. The period ha is paricularly noable from he graph is he accommodaive sance of year-ahead policy expecaions from mid-2001 o mid-2002, when he seing of he feral funds rae was view as being several percenage poins below is long-run level. Ineresingly, a he wo-year horizon his measure is much more sable han he measure (7). This finding indicaes ha he long-run level of he expec feral funds rae, *, is o a large exen adjusing in line wih he expecaion of policy wo years ahead. Such behavior is somewha puzzling, alhough i is consisen wih he findings of 21 Survey evidence indicaes ha marke paricipans saw a small risk of policy ighening a ha ime. Inde, a survey conduc by Money Marke Services on May 1, 1998 indica ha marke paricipans on average expec he feral funds rae o move from is level of 5.50 percen o a level of 5.51 percen a he subsequen FOMC meeing, 5.53 percen a he second meeing, and 5.59 percen a he hird meeing. 17

18 oher pars of he empirical finance lieraure ha longer-erm forward raes are highly volaile. 22 In Figure 9, he sance of policy measure (8) is shown for all horizons on he hree daes highligh above. Consisen wih he above discussion, he sance of policy was abou 175 basis poins below he anicipa long-run level of he feral funds rae in March 2002 and was expec o gradually move up o ha level. In January 2001, policy was view as being 125 basis poins above he long-run level and was expec o move mos of he way o he long-run level wihin a year. Lasly, policy was view as being only marginally above he long-run level in May How Imporan is Time Variaion? The above analysis presens evidence ha risk premia on fuures conracs are ime varying. To deermine how imporan his variaion is, he sandard deviaions of daily changes in he idenifi risk premia are compar o hose of he fuures raes hemselves in Figure 10. As is eviden, he risk premium accouns for lile of he variaion in he fuures rae for conracs wih shorer horizons. As he horizon exends, hough, he imporance of he risk premium increases. In fac, i evenually surpasses he sandard deviaion of he fuures rae, reflecing he negaive covariance beween he risk premium and expec policy a ha horizon (an observaion ha is discuss more in he nex secion). These resuls are consisen wih he examples shown earlier in Figure 7, in which he adjusmens o he policy pahs were small a firs bu cumula o larger amouns a 22 The finding is consisen wih he imporance of he level facor in explaining yield curve movemens, as poin ou by Lierman and Scheinkman (1991). The excess volailiy of long-erm raes has been discuss as far back as Shiller (1979). 18

19 longer horizons. Overall, hen, exracing policy expecaions under he assumpion of a consan risk premium may no be oo misleading for shorer horizons. However, a longer horizons, variaion in he risk premium is large enough ha i mus be aken ino accoun o accuraely measure he expec policy pah embd in fuures raes. Caveas The approach describ in his paper has he advanage of simpliciy. The idenificaion assumpion is easy o undersand, and he model can be solv by consrucing some simple porfolios of fuures conracs. However, ha simpliciy comes a some cos primarily ha he srucure of he risk premium is deermin using an ad-hoc procure. One could insead use a model o derive he srucure of he risk premium embd in fuures conracs, as in Jegadeesh and Pennacchi (1996). Such an approach has he advanage ha he risk premium is deriv from firs principles. However, ha approach has he disadvanage ha i mus place considerable srucure on he expec policy pah, unlike he porfolio approach describ above. 23 The deerminaion of he risk premium under he approach aken here involves some fairly srong assumpions. Among hem, i is diicul o undersand why he risk premium increases linearly a long horizons, especially considering ha he ineres rae is expec o have reach some long-run level. Neverheless, he posiive slope of he eurodollar fuures curve a long horizons is an empirical regulariy, and i seems even more implausible ha his paern can be aribu o policy expecaions. An imporan issue in his regard, however, is wheher he horizon a which policy expecaions are assum o level ou is suicienly long. One observaion ha is 23 For example, he ineres rae mus always rever o wha hey call he cenral endency a he same spe. 19

20 somewha concerning in his regard is ha he measur risk premium facor is negaively correla wih near-erm fuures raes. This correlaion may indicae ha he reversion of he shor rae o is long-run level akes longer han he four years assum. Inde, his would be consisen wih he resuls of Jegadeesh and Pennacchi (1996), who find ha i akes over four years for he shor rae o rever half way o is shor-run endency. 24 However, an alernaive inerpreaion is ha he negaive correlaion arises for economic reasons: Periods of economic weakness end o involve expecaions of lower ineres raes and higher risk premia. One could address his issue direcly by moving furher ou he erm srucure o derive he risk premium proxy. However, because he liquidiy of fuures conracs is fairly low a longer horizons, i would be advisable o derive he facor from he swaps curve in ha case. I leave ha exercise for fuure work. Conclusions Feral funds and eurodollar fuures conracs are perhaps he mos useful insrumens for deriving he expec pah of moneary policy from asse prices, given ha heir values are explicily i o shor-erm ineres raes and ha hey have considerable liquidiy over a wide range of horizons. However, he derivaion of policy expecaions is complica by he presence of risk premia on hose conracs. This paper demonsraes how o exrac he expec pah of policy under he assumpion ha he risk premia are consan over ime, and under a simple model ha allows he risk premia o vary. The resuls provide evidence ha he risk premia on hose conracs do, in fac, vary over ime. The impac of his variaion is 24 However, heir esimaes of he cenral endency in ha paper do no seem very plausible. 20

21 fairly limi for fuures conracs wih relaively shor horizons, bu i increases as he horizon of he conrac lenghens. In measuring he ime-varying risk premia, he basic idenificaion assumpion employ is ha policy expecaions level ou a some poin in he fuure. Inde, i seems unlikely ha marke paricipans hold srong views abou Feral Reserve policy acions aking place four years ahead or longer, and hence conracs expiring a such horizons should provide valuable informaion abou he risk premia embd in fuures raes. Of course, he analysis above is only one simple model of he behavior of he risk premia. Fuure research may be able o improve on he assum srucure of he risk premia, while reaining he basic approach o idenificaion aken in his paper. References Carlson, John B., Jean M. McInire, and James B. Thomson, Feral Funds Fuures as an Indicaor of Fuure Moneary Policy: A Primer, Feral Reserve Bank of Cleveland Economic Review 31, Goldman Sachs (2001), Message in he Marke, Fix Income Weekly Marke Oulook, April 20, Gürkaynak, Refe S., Brian Sack, and Eric Swanson (2002), Marke-Bas Measures of Moneary Policy Expecaions, Finance and Economics Discussion Series Working Paper # , Board of Governors of he Feral Reserve Sysem. 21

22 Jegadeesh, Narasimhan and George G. Pennacchi (1996), The Behavior of Ineres Raes Impli by he Term Srucure of Eurodollar Fuures, Journal of Money, Cri, and Banking 28, Krueger, Joel T. and Kenneh N. Kuner (1996), The F Funds Fuures Rae as a Pricor of Feral Reserve Policy, Journal of Fuures Markes 16, Lange, Joe, Brian Sack, and William Whiesell (2002), Anicipaions of Moneary Policy in Financial Markes, forhcoming, Journal of Money, Cri, and Banking. Lierman, R. and Scheinkman, J. (1991), Common Facors Aecing Bond Reurns, Journal of Fix Income 1, Roberson, John C. and Daniel L. Thornon, Using Feral Funds Fuures o Pric Feral Reserve Acions, Feral Reserve Bank of S. Louis Review 78, Rudebusch, Glenn (2002), Term Srucure Evidence on Ineres Rae Smoohing and Moneary Policy Ineria, forhcoming, Journal of Money, Cri, and Banking. Shiller, Rober J. (1979), The Volailiy of Long-Term Ineres Raes and Expecaions Models of he Term Srucure, Journal of Poliical Economy 87, Södersröm, Ulf (2001), Pricing Moneary Policy wih Feral Funds Fuures Prices, Journal of Fuures Markes 21,

23 Table 1 Esima Risk Premia Levels and Loadings Conrac Consan Risk Premium (Basis Poins) Loading on Slope Facor ( (i) or (i) ) Feral Funds Fuures (monhs ahead) Eurodollar Fuures (quarers ahead)

24 Figure 1 Average Shape of Fuures Curves Percenage Poins Eurodollar Fuures Feral Funds Fuures Quarers Ahead Average level of feral funds and eurodollar fuures raes from 1992 o 2002, express relaive o he average level of he overnigh feral funds rae.

25 Figure 2 Expec Policy Pah under Consan Risk Premium March 20, 2002 January 2, 2001 May 1, Quarers Ahead

26 Figure 3 Raes on Basis Swaps One-year Three-year Five-year Basis Poins Jan May Sep Jan May Sep Jan May Sep Jan May Sep Jan May Sep Jan May

27 Figure 4 Term Srucure of Eurodollar Fuures Raes March 20, Dec-01 Dec-02 Dec-03 Dec-04 Dec-05 Dec-06 Dec-07 Expiraion Dae

28 Figure 5 Term Premia Facor Basis Poins Per Monh Jul-92 Jan-93 Jul-93 Jan-94 Jul-94 Jan-95 Jul-95 Jan-96 Jul-96 Jan-97 Jul-97 Jan-98 Jul-98 Jan-99 Jul-99 Jan-00 Jul-00 Jan-01 Jul-01 Jan-02

29 Figure 6 Policy Expecaions Measure (7) One Year Ahead Two Years Ahead Targe Feral Funds Rae 0.00 Jul-92 Jan-93 Jul-93 Jan-94 Jul-94 Jan-95 Jul-95 Jan-96 Jul-96 Jan-97 Jul-97 Jan-98 Jul-98 Jan-99 Jul-99 Jan-00 Jul-00 Jan-01 Jul-01 Jan-02

30 Figure 7 Comparison of Policy Pahs 5.00 March 20, Consan Term Premium Time-Varying Term Premium Quarers Ahead 6.00 May 1, Consan Term Premium Time-Varying Term Premium Quarers Ahead

31 Figure 8 Policy Expecaions Measure (8) Percenage Poins /1/92 1/1/93 7/1/93 1/1/94 7/1/94 1/1/95 7/1/95 1/1/96 7/1/96 1/1/97 7/1/97 1/1/98 7/1/98 1/1/99 7/1/99 1/1/00 7/1/00 1/1/01 7/1/01 1/1/ One Year Ahead Two Years Ahead -4.00

32 Figure 9 Measure (8) on Selec Daes March 20, 2002 January 2, 2001 May 1, 1998 Percenage Poins Quarers Ahead

33 Figure 10 Sandard Deviaion of Daily Changes January 1992 o June 2002 Basis Poins Fuures Rae Risk Premium Quarers Ahead