Using Federal Funds Futures Contracts for Monetary Policy Analysis

Using federal funds futures contracts for monetary policy analysis ∗ Refet S. Gürkaynak rgurkaynak@frb.gov Division of Monetary Affairs Board of Governors of the Federal Reserve System Washington, DC 20551 June 5, 2005 Abstract Federal funds futures are popular tools for calculating market-based monetary policy surprises. These surprises are usually thought of as the differencebetweenexpectedand realized federalfundstargetratesat the currentFOMCmeeting. Thispaperdemonstratestheuseoffederalfunds futures contracts to measure how FOMC announcements lead to changes in expected interest rates after future FOMC meetings. Using several ‘surprises’ at different horizons, timing, level, and slope components of unanticipated policy actions are defined. These three components have differing effects on asset prices that are not captured by the contemporaneous surprise measure. The opinions expressed are those of the author and do not necessarily reflect the views ∗ of the Board of Governors or other members of its staff. I thank Brian Sack and Eric Swanson for many discussions on monetary policy surprises, and Ben Bernanke, Ken Kuttner, and Jonathan Wright for useful suggestions. Andrea Surratt provided outstanding research assistance.

1 Introduction Measuring the effects of monetary policy on asset prices is a tricky task. Both the policy tool, the federal funds rate, and other asset prices are jump variables, which makes it difficult to come up with reasonable identifying assumptionsinmonthlyorquarterlyanalysis. Economists,atleastsinceCookand Hahn (1989), have been trying to overcome this hurdle by running eventstudy regressions using higher frequency (usually daily) data. Cook and Hahn had used the raw policy action as independent variable in their study. However, we expect asset prices to only react to the unanticipated policy action, which necessitates measuring the policy surprise. To isolate policy surprises, calculating the unanticipated part of the policy actionfrommarket-basedmeasureshasrecentlybecomepopularintheacademic literature, federal funds futures being the most commonly employed securities for this purpose (see Kuttner, 2001, for an important early contribution). This literaturefocusesoncalculatingveryshorthorizonsurprises,mostoftenthesurpriseassociatedwiththefundsrateexpectedtoprevailuntilthenextperiod,the next Federal Open Market Committee (FOMC) meeting. However, the FOMC maygivedifferentpolicysignalspertainingtolongerhorizonsbythestatement, or investors can infer different signals based on the state of the business cycle. Ahawkishstatementaboutfutureinterestratechanges,forexample,cancounterweightheeffectsofaneasingsurpriseonexpectationsaboutfundsratesafter the next meeting. That is, a single FOMC policy announcement can contain different policy ‘surprises’ for different horizons. Papers that use changes in expectations at longer horizons to capture a relatively more permanent surprise, such as Bernanke and Kuttner (2005), use changes in expectations in a future month. But Federal Reserve’s interest rate decisions are not made monthly. For example, a three month time period can span one or two FOMC meetings. 1

As interest rates change almost exclusively at scheduled FOMC meetings, the natural horizon for thinking about interest rate changes is in terms of FOMC meetings.1 Thispaperuseslong-maturityfederalfundsfuturescontractstoextractpolicy expectations and surprises at horizons defined by future FOMC meetings. SincetheFOMCscheduleisknowninadvance,itispossibletousethecontracts expiring in the months of future FOMC meetings to measure market-based expectationsforthesemeetingsand,ofcourse,changesintheseexpectations(surprises at longer FOMC meeting horizons) due to FOMC announcements. The first part of the paper demonstrates the mechanics of these calculations. In the second part of the paper the “surprises at FOMC meeting horizons” ideaisputtoworkforanempiricalapplication. Usingthepolicysurpriseforthe current funds rate decision, and changes in expected funds rates after the next andthefollowingFOMCmeetingsonthedayofthecurrentpolicyaction,policy surprises can be decomposed into timing, level, and slope components. Level surprises are the relatively lasting changes in policy expectations, measured as the changes in expected rates after the next FOMC meeting. Timing surprises, ontheotherhand,areconstructedtohavenoeffectontheexpectedfundsrates afterthenext meeting, while slopesurprisesare changes in expected rates after the second FOMC meeting that are over and above the level surprise. Thinking about different types of monetary policy surprises and measuring monetary policy as a multi-dimensional process are novel. Hamilton and Jorda (2002) recognize the discrete nature of policy actions and differentiate between macroeconomic effects of an unanticipated policy change and a policy inaction when a policy change was expected. Using a factor model Gürkaynak, Sack, andSwanson(2005b)showthatmonetarypolicyischaracterizedbytwofactors ratherthanasingleoneandtheyidentifythetwodimensionsofmonetarypolicy 1Intermeeting policy actions were especially rareafter1994. 2

using a factor rotation.2 Whilemeasuringmonetarypolicysurprisesatdifferenthorizonsfromfederal fundsfuturescontractsisageneralmethod,interpretingthosesurprisesrequires imposing some structure. The timing/level/slope decomposition proposed in this paper is onesuch structure and the empiricalanalysis shows thatthe three surprise components’ effects on asset prices are consistent with their names. Timing has no effect on asset prices other than short-maturity yields, while level has a large effect on all asset prices. The conventional measure of policy surprises,thesurprisetoexpectedfundsratesinthecurrentintermeetingperiod, understates the effects of monetary policy on asset prices because this surprise measure is a combination of timing and level. The slope component is also estimated to have a significant effect on long-term yields. 2 Federal funds futures contracts Federal funds futures are contracts with payouts at maturity based on the average effective federal funds rate during the month of expiration. These securities have been trading on the Chicago Board of Trade (CBOT) since late 1988. The value of the contract at expiration is 100 r¯, where r¯is the average − effective federal funds rate over the expiry month.3 Contracts with expiration maturities out to two years are offered, but most of the trading takes place in contracts with expiry dates within six months. Prices of these contracts are clearly related to expectations of target federal funds rates, which makes them useful for policy analysis. There are many other securities that have payouts tied to the funds rate in some way, such 2Craine and Martin (2004) also use a factor model to analyze the policy transmission mechanism,extendingtheheteroskedasticitybasedidentificationmethodofRigobonandSack (2002). 3Inshowingthemechanicsofusingfederalfundsfuturestocalculatemonetarypolicysurprisesbelow,itisassumedthateffectivefundsratesareequaltotargetrates. Thisassumption simplifiesnotation and does notmake a substantive difference. 3

as commercial paper and eurodollar deposits; however, Gürkaynak, Sack, and Swanson (2002) show that for horizons up to six months investors’ forecasts measured using the federal funds futures rates outperform all other marketbased measures in predicting actual future funds rates. This justifies using federalfundsfuturestogaugepolicyexpectationsasrationalexpectationswould incorporate the best forecast. Federal funds futures can be used to calculate levels and changes of interest rate expectations for any date within the maturity of the futures contracts. These contracts were introduced to the literature by Krueger and Kuttner (1996), Rudebusch (1998), Söderström (2001) and popularized by Kuttner (2001). Below, the implied rates from these securities’ prices are employed to calculate market-based measures of the surprise associated with the current policy decision, and changes in expected rates after the next and further away FOMC meetings around the current meeting, as well as to generate marketbased measures of levels of expected interest rates for horizons encompassing a given number of FOMC meetings. 3 Using federal funds futures contracts 3.1 Basics Calculatingexpectationsandsurprisesfromfederalfundsfuturescontracts requires introducing some notation first. In what follows, subscript t denotes time, in days or at a higher frequency. For convenience, think of date “t” as a policy date, so that changes in prices of federal funds futures on this day are duetoFOMCactions. PolicydatereferstodatesofscheduledFOMCmeetings (regardless of a policy change taking place or not) and dates of intermeeting 4

policy actions.4 FOMC meetings are indexed by j, with j = 0 the current meeting j = 1 the next scheduled meeting, etc., and i(j) denotes how many monthsawaythejthFOMCis,startingwith0forthecurrentmeeting. Therate implied by the federal funds futures contract is fi(j), for the contract expiring t ini(j)months. Finally,letd denotethedayofthejth FOMCmeetingandm j j the number of days in that month. Having introduced the notation, it is also important to spell out a key assumption explicitly: throughout the paper it is assumed that on policy dates future intermeeting moves are seen as zero probability events. This assumption is reasonable given the infrequency and unexpectedness of intermeeting policy actions.5 It is required because the analysis below is carried out at FOMC meetingfrequencyusingdatesoffuturemeetingsand, ofcourse, datesoffuture intermeeting moves are not known in advance. Afinalnoteaboutthereferencestotimeperiodsinthispaperareinorder,for clarity. The federal funds futures prices are time series data. Frequency refers to the observation interval of this data. At each point in time, prices of all federal funds futures contracts currently trading are observed. These contracts coverdifferentmonths,referredtoasmaturities,orexpirations. Finally,ateach pointintime,lookingahead,investorsthinkaboutwhatwillhappentointerest rates at different FOMC meeting horizons. “Horizon” refers to expectations about different points in time, but all of these expectations are formed today. Similarly, when the discussion is about changes in expectations (surprises) at different horizons, it should be clear that all these surprises take place today, on the day of the current FOMC meeting. To use the futures contracts for monetary policy analysis we start with the 4Ofcourse,with intraday data the policy date refersto the policy announcementtime. 5Intermeeting policy actions took place relatively more often in the pre-1994 period. In the empirical part of this paper the post-1994 sample is used to check for robustness of the results. 5

simplestcase,constructingthesurprisecomponentofthecurrentpolicydecision forthespotrate,andthenextendtheanalysistochangesinexpectationsabout future interest rates. 3.2 Current policy surprise Calculating monetary policy surprises by using federal funds futures rates was brought to the forefront of policy analysis by Kuttner (2001). In this subsection we follow him to show the relationship between federal funds futures ratesandtheFOMCpolicydecision. OnthedaybeforetheFOMCmeetingthe arbitrage-freepriceof thespot-monthfederalfundsfuturecontractwill satisfy6 d m d f0 = 0 r + 0 − 0E (r )+µ0 , (1) t − 1 m 0 − 1 m 0 t − 1 0 t − 1 where r is the target federal funds rate prevailing before the meeting and 1 − r is the target rate after the meeting.7 The quantity µ0 represents a term- 0 t 1 − premium for the spot-moth contract, which will be discussed later. Apart from the term premium, the spot month federal funds futures rate is equal to the expectedaveragetargetrateoverthemonth, givenbythetheweightedaverage ofthetwotargetrates.Afterthepolicydecisionisknown,attimet,theimplied futures rate is d m d f0 = 0 r + 0 − 0r +µ0. (2) t m 0 − 1 m 0 0 t Using equations (1) and (2), the unanticipated component of the monetary policy action, call it e0, is given by t m e0 r E (r )= f0 f0 µ0 µ0 0 . (3) t ≡ 0 − t − 1 0 t − t − 1 − t − t − 1 m 0 d 0 − £¡ ¢ ¡ ¢¤ 6SeeGürkaynak,Sack,and Swanson (2002)fora derivation from firstprinciples. 7Note again that we are assuming that effective funds rates are equal to the target rate. Otherwise r 1 should be replaced by the average effectiverate so far in the month. − 6

Notethattheprevioustargetrate(observedeffectivefundsratesuntilthepolicy date)dropsoutduetothedifferencing. Thisiswhyassumingthateffectivefunds ratesareequaltothetargetratesisasimplifyingassumption,aslongasagents do not expect future effective rates to differ from target rates. Backingoutthepolicysurprisefromfuturesprices requiresmakingarather weak assumption about the behavior of the term premium. Assuming that the high frequency change (the change around the policy action) in the term premium is negligible, the unanticipated policy action is m e0 = f0 f0 0 , (4) t t − t − 1 m 0 d 0 − ¡ ¢ which is the scaled change in the futures rate around the policy action. Scaling is necessary because the surprise is only relevant for the remaining part of the month.8 Thismeasureofpolicysurprise,e0,wasreferredtoasthe“theunanticipated t component of policy,” or “the policy surprise” in previous studies such as Kuttner(2001),Gürkaynak,Sack,andSwanson(2005a)andBernankeandKuttner (2005). Later in this paper policy surprises for different horizons and different types of surprises are discussed. To avoid confusion, in this paper e0 is referred t to as the “current policy surprise” or “the surprise associated with the current policy setting.” Itisimportanttonotethattheassumptionmadeaboutµinthecalculation of e0 does not rule out time-varying term premia. Low frequency variation t in the futures term premium (for example due to cyclical factors, as argued in Piazzesi and Swanson, 2004) would not affect the calculation of the policy surprise. Itisthehighfrequencyvariation(variationaroundthepolicydate)in the term premium that should be small. Specifically, the term premium should 8For policy dates on the first day of the month, the relevant futures rate at time t 1 (assuming daily data)isf1 and thepolicy surprise is calculated ase0=f0 f1 . − t t − t − 1 7

not respond to the policy action. The scaling factor adds a complication to this assumption. For a policy actiononthelastdayofamonth,forexample,thechangeinthetermpremium is multiplied by 30, amplifying the noise in the measurement of the e0 surprise t greatly. To get around this problem Kuttner (2001) suggests using the next month’s contract when a policy action takes place in the last three days of the month. In this case e0 = f1 f1. There is no scaling involved because the t t − policy action affects the expected rates in the entire subsequent month (When the FOMC meetings are late in the month, there are no scheduled meetings in the subsequent month). In the applied part of this paper (section 4), the following month’s contract is used whenever the scale factor is greater than four, approximately corresponding to the last week of the month. 3.3 Changes in expected rates at longer horizons Thepolicysurprisemeasure given by equation (4)adequately captures the surprise associated with the current target funds rate decision. If all policy surprises in policy actions change expected rates in the short-run in the same way, this is all that one would need. However, it is conceivable that different policyactions,eveniftheyleadtothesamecurrentpolicysettingsurprise,have differentimplicationsabout thenear-termpathof monetarypolicy. Addressing such issues require measuring changes in policy expectations at slightly longer horizons. One way of doing this is to use changes in, say, f3. This would pick up how much interest rate expectations three months away have changed, but, in some observations there will be one scheduled FOMC meeting in three months time, insomeotherstherewillbetwo. Thescopeforratechangesismorewhenthere are two meetings, compared to when there is only one. Thus, this measure will 8

not consistently capture changes in expectations at the same FOMC meeting horizon. A better way, given the FOMC meeting frequency of interest rate target decisions, is to calculate how much the expected interest rate after the next (or a further away) FOMC has changed. This calculation requires knowledge of the dates of future FOMC meetings, which are available extending out to at least three meetings at any point in time. The day before the current meeting, the federal funds futures contract encompassing the next meeting has the implied rate d m d fi(1) = 1 E (r )+ 1 − 1E (r )+µ1 . (5) t − 1 m 1 t − 1 0 m 1 t − 1 1 t − 1 The implied rate is a weighted average of the expected target rate after this meeting(whichisexpectedtoprevailuntilthenextmeeting)andthetargetrate expected to be the outcome of next FOMC meeting. Leading this equation one period and differencing, the change in the expected target rate after the next FOMCmeetingduetothecurrentpolicyannouncement,e1 E (r ) E (r ), t ≡ t 1 − t − 1 1 is d m e1 = fi(1) fi(1) 1 e0 1 , t ∙³ t − t − 1 ´ − m 1 t ¸ m 1 − d 1 which once again assumes that µ1 µ1 is negligible. t − t − 1 Changes in interest rates expected to prevail after future FOMC meetings canbecalculatedaslongas thedateofthefutureFOMCisknownandthereis tradinginthefederalfundsfuturescontractcoveringthemonthofthatmeeting. The change in the expected interest rate after the nth FOMC meeting due to the current policy announcement is d m en = fi(n) fi(n) n en 1 n . (6) t ∙³ t − t − 1 ´ − m n t− ¸ m n − d n Note that the scale factor depends on when in the month the nth meeting is, 9

not on when the current meeting is. If the scale factor is large (for meetings thatwilltakeplace towards the endof amonth), the change inexpectedfuture interest rates can be calculated as en =fi(n)+1 fi(n)+1. t t − t − 1 3.4 Interest rate level and policy expectations Although the usual object of interest in policy analysis is the policy surprise as measured by changes in expected rates, federal funds futures can also be used to calculate expected interest rates and expected policy moves. Of course, calculating the expected rates after several FOMC meetings is the essence of calculating the surprise at these horizons. The surprise, after all, is the change in the expected rates on the policy date. The expected interest rate on the day of current meeting, t, using equation (5), is9 d m E (r )= fi(1) 1 r µi(1) 1 . (7) t 1 t − m 0 − t m d ∙ 1 ¸ 1 − 1 Importantly, in calculating expected levels of interest rates, the term premium does not drop out because there is no differencing involved. Gürkaynak, Sack, and Swanson (2002) estimate the term premium in federal funds futures contracts to be very small, about one to three basis points per month, which can be used to substitute for µi(j).10 Expected interest rates at longer horizons can similarly be calculated recursively, with the expected interest rate after the jth FOMC given by d m E (r )= fi(j) j E (r ) µi(j) j . (8) t j ∙ t − m j t j − 1 − t ¸ m j − d j 9Ifthiscalculationisdoneattimet 1,beforetheoutcomeofthecurrentFOMCmeeting − is known, Et 1(r0) has to be estimated first using the known r 1, as described in equation (8). Here, it−would matter if observed effective funds rates are d−ifferent from target rates. If the difference is noticeable (which happens rarely) the observed average effective rate in the currentmonth untiltoday can besubstituted forr 1. 10AlsoseeDurham(2003)andSack(2004)about−theterm-premiuminfederalfundsfutures. 10

Calculating the expected rates at different FOMC horizons and plotting these makes a beautiful step-path. Figure 1 shows the step-path on August 12 and August 13, 2002, an FOMC meeting day. This was a time when the FOMC was aggressively cutting rates, thus expected rates were lower at longer horizons. The changes in expected rates in the day of the meeting are the policy surprise measures (the ej’s) calculated above. On August 13, 2002, the current policy surprise was positive although the target rate was not changed. Investors had attributed positive probability to a 25 basis point easing that did not materialize. On the other hand, expected rates after more distant FOMC meetings moved in the opposite direction and fell some. Thus, on this date the positivecurrentpolicysurprisewasnotindicativeofhowshort-runinterestrate expectations changed. This differential response of expectations at different horizons to monetary policy surprises will be analyzed in detail in section 4 below. Equipped with equation (8), it is easy to calculate expectations about future policy actions, E (r r ), by simply differencing equation (8) for two t j j 1 − − consecutive expected rates, which yields the difference equation11 m E (r r )= fi(j) E (r ) µi(j) j . (9) t j − j − 1 t − t j − 1 − t m j d j h i − Theexpectedpolicyactionsaretheheightsofthestepsinfigure4. Inparticular, the next expected policy action is m E (r ) r = fi(1) r µi(1) j . (10) t 1 − 0 t − 0 − t m d j j h i − Thus, we can calculate not only what the expected funds rate is at some future date, but also the expected pace of getting there. 11Notethatthisis a difference equation in j,notin time. 11

Given the expected rates at FOMC horizons as a time series, other policy expectations related quantities can also be calculated. For example, it is trivial tocalculatehowmuchtheexpectationsaboutthenextpolicyactionhaschanged onthedayofthecurrentFOMCmeeting,bydifferencingequation(9)overtime. Thissectiondemonstratedthattheusefulnessoffederalfundsfuturesextend beyond calculating the surprise associated with thecurrentsetting ofmonetary policy and showed ways of extracting more information from these contracts. The next section provides an empirical application using policy surprises at longer horizons. 4 Decomposing policy surprises 4.1 Timing and level Therecenteventstudyliteratureonmeasuringtheeffectsofmonetarypolicyon assetprices(Kuttner,2001, BernankeandKuttner,2005, Gürkaynak, Sackand Swanson, 2005b) uses regressions of the form ∆y =α+βsurprise +ε , (11) t t t where∆y isthechangeintheassetpriceorreturnaroundthepolicyannouncet ment and ε captures the changes in y that are not due to monetary policy. t t Although the standard in this literature is to use daily observations, Gürkaynak, Sack and Swanson (2005b) construct an intraday data set and show that there are considerable gains in precision from using intraday data. The empirical exercises in this paper employ this data set, measuring changes in asset prices (including federal funds futures) in a thirty-minute window around the policy announcement, starting from ten minutes before the event, and ending twenty minutes after. Note that the policy announcement was an implicit an- 12

nouncement before 1994, when markets had to infer the change in the policy stance from the following day’s open market operation. The measurement window is around the point in time when policy news reach financial markets (the announcement time), rather than when the policy decision is actually made. e0,e1,ande2 aremostoftencalculatedfromthefirst,third,andfifthfederal fundsfuturescontracts. Thefirstandthirdcontracts’liquidityislowintheearly 1990s, but it increases substantially starting from 1994, while the fifth contract is very illiquid before 1998. In the empirical part of this paper, analysis is carried out for the full sample when only e0 and e1 are used and results for the post-1994 sample are presented as a robustness check. The sample is limited to post-1998 when e2 is also employed. In regressions of the form (11), using e0 as the policy surprise measure is commonasthiscapturesthesurpriseassociatedwiththecurrentsettingofpolicy,theusualdefinitionofpolicysurprise. However,someauthorspreferchanges inlongerdatedsecurities, suchasthreemontheurodollarfutures (Rigobon and Sack,2002),orthechangeinthethirdfederalfundsfuturesrate,f3,(Bernanke and Kuttner, 2005) instead of e0 or as a robustness check. The reason for using changes in expected rates at longer maturities is to capture relatively more permanentchanges in expected interestrates, rather than surprises that have a small impact on expected rates in the near future. Consider a stylized example where, say, at the end of a tightening cycle financial markets expect one last 25 basis point target rate increase. Assume that investors attach equal probability to the tightening taking place in this meeting or the next one (but certainly one or the other), and then expect no further changes. If the last tightening takes place in this meeting, it will be a positivetightening surprise(12.5 basis points) as measured bye0, but expected rates after the next FOMC will not change, that is, e1 will be zero.12 The 12If the policy move does nothappen in the current meeting,itwillbe measured as a 12.5 13

implications of this surprise for asset prices is likely to be very different from a 12.5 basis point current policy setting surprise that leads investors to revise up their expectations of the funds rate in the near future in a parallel fashion. This transitory versus permanent surprise idea can be formalized better by definingapuretiming surprise. Anobvious(butcertainlynottheonlypossible) definition of a timing surprise is a policy surprise that leaves expected interest rates after the next FOMC unchanged. With this timing construct, the change inexpectedratesafterthenextmeeting,e1,wouldnothaveatransitorycompot nent by definition. In this case, e1 can be thought of as providing a measure of t the parallel shift of interest rate expectations, i.e. as defining a level surprise.13 That is e0 = α level +timing , (12) t 1 t t e1 = level . (13) t t A regression of e0 on e1 will decompose the surprise in the current policy ant t nouncement into level and timing components, where timing will be the residual.14 This way of ‘defining’ different types of monetary policy surprises is similar in spirit to VAR identification. Timing is essentially constructed by a zero restriction. Similar to identified VARs, one can think of alternative identifying assumptions. For example, level can be defined as, say, e3, and timing as the component of e0 that is orthogonal to e3. The timing and level constructs used in this paper are the probably the most intuitive ones and in section 4.1.1 it will be shown that the two components behave in a way that is consistent basis pointsurpriseeasing in termsofe0,bute1 willagain be zero. 13Gürkaynak,Sack,andSwanson(2002)alsoproposeasimilartiming/leveldecomposition, butthatpaperdoes notinvestigateassetprice implicationsofthe two types ofsurprises. 14Although equations (12) and (13) are exact, in reality the prices of federal funds futures contractsandthesurprisemeasuresconstructedfromthemarelikelytoincludesomeidiosyncratic noise. This will cause the coefficient estimates in regressions using these measures on the right hand side to be biased down some. The same potential errors in variables problem alsoapplies to analysesusinge0 orothermarket-based surprises on the righthand side. 14

with their names. Note that the level and timing components constructed this way, like fundamental VAR shocks, will be orthogonal to each other. Table 1A reports the results of the regression that decomposes e0 into level and timing. The R2 (at 47%) suggests that timing surprises constitute a large part of the current policy surprise. The coefficient on level is not significantly different from unity, which is consistent with defining level as a parallel shift of short-term expected interest rates. 4.1.1 Asset price responses to timing and level surprises Theassetpriceresponsetotimingandlevelsurprisescanbestudiedbyextending regression equation (11), to include two surprise variables: ∆y =α+β timing +β level +ε . (14) t 1 t 2 t t Regressions of the from (14) pose a difficulty in calculating the standard errors because timing is a constructed variable. To calculate reliable standard errors that take account of the variation stemming from the first step regression(estimationoftiming)theregressioncoefficientsarebootstrapped. Ineach bootstrap replication e0, e1, and the left-hand side variable are sampled togetherandtimingisestimatedforthatsample,whichisthenusedinestimating equation (14). This procedure is repeated 1000 times and standard errors of coefficients in (14) are calculated as the standard deviation of the distribution resulting from the bootstrapping exercise.15 Bootstrapped standard errors are larger than OLS standard errors, as expected. The results of the regressions are presented in table 1B, where results using thestandardmonetarypolicysurprise,e0,arealsopresentedforreferenceinthe 15Significance tests are based on normal approximation, which agree with the percentile method in almostallcases. 15

first column.16 This current policy setting surprise has a large and statistically significant effect on Treasury yields, with the effect becoming smaller as the horizon increases. The timing surprise also has a large and statistically significant impact on shorter-term yields. Although short lived, the timing surprise does haveamechanicaleffect on yields that is important at short horizons. Assumingthattheaverageduration ofatimingsurpriseis1.5months(12months divided by 8 scheduled FOMC meetings a year) a one percentage point timing surprise should move the three-month yield by 50 basis points, which is about the estimated effect. The effect of the timing surprise declines as the maturity increases (the effect is not significantly different from zero at five and ten year horizons), and its explanatory power declines even faster (the R2 falls to seven percent for the two-year yield).17 Thelevelcomponentofmonetarypolicysurpriseande0haveaboutthesame effect on the three month yield. Differentiating between level and timing does not matter much at this maturity because timing itself has a sizable impact. However, as maturity lenghtens the choice of the policy surprise measure becomes important. Since the current policy setting surprise is a combination of the timing and level surprises, and the timing surprise has no effect on longer term yields, the e0 measure understates the effects of a shift in the monetary policy stance on these yields. The point estimates when the policy surprise is measuredbylevelsurpriseareuptofifteenbasispointshigherthanthoseusing the current policy surprise. Using the level surprise also improves the explanatory power of the regressions, as can be seen from the increased R2 statistics. 16ThesamplestartsinJuly1991becausetheintradaydataonon-the-runTreasurysecurities that are on the left-hand side of these regressions are available only since this date. Two outliers, the policy actions on January 3, 2001 and September 17, 2001 are excluded, the former because of the outsized stock price movement that day, the latter because of the volatility in financialmarketsunrelated to monetary policy. 17The large and significanteffectofthe timing surprise on the two year yield is surprising, even though the R2 is very low. This seems to be due to a few high-leverage observations, and itis notpresentin the post-1998 sample,discussed below. 16

The bottom row of table 1B reports the effects of e0, timing, and level surprises on stock prices, measured by the percentage change in S&P 500. The effectusinge0 isestimatedtobe-2.93percent,whileitis-3.85percentusingthe levelsurprise. Employingthecurrentratesurpriseasthepolicysurprisemeasure understates the effect of monetary policy on stock prices by a percentage point as the timing component has a small and insignificant effect.18 Tables 2A and 2B repeat the same exercise for a shorter sample starting at 1994. The results are robust to this change of sample; most of the estimated parametersareaboutthesameasthoseforthefullsample. Anotableexception is the stock price regression where the coefficients of both the current rate surprise and the level surprise are larger (in absolute value). In general, it seems thattherelativelylowerpre-1994liquidityofthefederalfundsfuturescontracts usedintheconstructionofthee0,timing,andlevelsurpriseshasnotinfluenced the full sample results. Overall, it turns out that timing has a significant effect only on short-term yields and for that reason differentiating between timing surprises and level surprisesdoesmakeadifference. The“policysurprise”conceptdoesnotusually refer to timing surprises, but its usual empirical counterpart, e0, often includes timingaswellaslevelsurprisesandthereforeunderstatestheeffectsofmonetary policy on asset prices. 4.2 Timing, level, and slope The decomposition presented above assumed that policy surprises consist of only timing and level components. This assumption is overly restrictive, as the FOMC is able to shape future policy expectations with the statements it releasesafteritsmeetings(Gürkaynak,Sack,andSwanson2005b,Ellingsenand 18The parameter estimates presented here are not directly comparable to Bernanke and Kuttner(2005)due to differentsample periods,butare in line with theirresults. 17

Söderström 2001, 2003). These statements often lead to revisions to expected pace of interest rate changes, that is, it is likely that policy surprises have a slope component as well as level and timing components. This paperidentifies slope in amannersimilar toits treatment of timing—as a residual. If e0 consists of level and timing and e1 is only level (an assumption that worked well above), a longer-dated change in expected interest rates is needed to identify slope. For this purpose e2 is used. Specifically, timing, level, and slope areidentifiedusing changes in expectedrates atthreehorizons, assuming that e0 = α level +timing , t 1 t t e1 = level , t t e2 = α level +slope . (15) t 2 t t It should be emphasized again that this decomposition, like the timing vs. level decomposition carried out in section 4.1, is one of many ways one could think about timing, level, and slope. These components are empirical constructs, and given this specific way of constructing them, they may not behave in a way consistent with their names but it turns out that they do. We had seen above that timing and level do indeed behave like a transitory and a more permanent surprise. Now we turn to the econometric analysis in the post-1998 sample, adding slope as a third policy surprise component. Table 3A shows the results of the two regressions used in the construction of timingandslopesurprises, againusinge1 aslevel. Thefirst regression shows thatthecoefficientofleveline0 isstillnotstatisticallydifferentfromunity,and alsothatthecontributionof timing(theresidual)tothecurrentpolicysurprise is somewhat smaller in this more recent sample—R2 is 68 percent rather than the 47 percent before. 18

The second regression is for constructing slope. Slope is estimated as the residual of regressing e2 on level and timing. Although it is not present in equation (15), timing is included in this regression to ensure that the three components of policy surprises are orthogonal to each other. Consistent with the definition of timing as the component of the policy surprise that does not change expected interest rates after the next FOMC meeting, the coefficient of timing on e2 (change in expected rates after the second FOMC meeting) is not significantly different from zero. Like timing, level also behaves as its namesuggests, withacoefficientnotsignificantlydifferentfromunity.19 About 20 percent of the variation in e2 is due to slope. The four panels of Figure 2 showthecurrentpolicysurpriseandthetiming,level,andslopesurprisesinthe post-1998 sample. 4.2.1 Asset price responses to timing, level, and slope surprises The effects of the three factors on asset prices are presented in Table 3A, using regressions of the form ∆y =α+β timing +β level +β slope+ε , (16) t 1 t 2 3 t where the standard errors are once again bootstrapped. For each bootstrap samplefirsttiming,thenslopeisestimatedandthentheseareusedinestimating (16). Standard errors are calculated from the distributions of 1000 bootstrap estimates. Theeffectsofthecurrentpolicysurprise(e0),timing,andlevelaresimilarto thosereportedinTable1Bforthefull1991-2004sample. Thenotabledifferences arethemuchsmallerandinsignificantcoefficientoftimingonthetwo-yearyield, theinsignificanceofe0andlevelontheten-yearyield,andthelargerimpactofe0 19Notethatthestandarderrorsinthesecondregressionarebootstrappedusingthemethod described in section 4.1.1. 19

andlevelonthestockprices. Findingthattimingdoesnotsignificantlyaffectthe two-yearyieldisexpectedasitsearlierlargeandsignificantcoefficientwasdueto ahandfulofhighleverageobservationsthatdropoutinthissample. Gürkaynak, Sack, and Swanson (2005a) show that the effect of e0 on long forward rates is negative, which would offset the positive effect of these surprises on short term yields when the ten-year yield is the object of analysis. This effect seems to be stronger in the more recent sample, leading to the insignificant coefficient. The effects of the slope surprise are shown in the right-most panel of table 3B.Slopehasarelativelysmalleffectonthethree-monthyield. Onmostpolicy dates, the slope component of monetary policy surprise refers to changes in expectations further away than three months, thus this small coefficient is to be expected. Its effect is much larger than the effects of level for the two- five-, and ten-year yields, significant at all maturities. The slope surprise appears to help shape expectations of interest rates extending to long horizons. On the other hand, the effect of the slope surprise on S&P 500 is insignificantly differentfromzero(althoughthepointestimateisnotsmall). Thismaysuggest thatslopereflectsthemarkets’readingoftheeconomicoutlookfromthepolicy announcement, together with the implied policy path. If the central bank is signalinghigherratesinthenearfutureduetoinflationaryworries,stockprices will fall, if the outlook is for a rapidly growing economy, stock prices will be supported by this. To the extent that the slope surprise is a mixture of these two,itseffectonstockpriceswillbeambiguous. Fixed-incomeyields,ofcourse, will go up in either case. In this paper, slope is calculated using changes in expected rates out to about five months. This assumes that changes in expected rates within this horizon reflect investors’ direct inference about the interest rates from the policy announcement (the exogenous policysurprise given their information about 20

the central bank’s preferences and the state of the economy), while changes in longer-term rates are responses to these policy surprises. The distinction between what is a policy surprise and what constitutes a response to this surprise is, admittedly, somewhat arbitrary. Inanotherpaperthatpursuesasimilaridea,Gürkaynak,Sack,andSwanson (2005b)assumethatallchangesinexpectedrateswithinaone-yearhorizonare reflections of the forward looking signal associated with the policy announcement, while changes in expected rates with longer maturities are responses to these. They use this assumption to do a factor decomposition and create a target and a path factor surprise, without dwelling on the timing component. Their target factor is similar to e0, while the path factor behaves like the slope componentcalculatedfromchangesinexpectedratesaboutayearahead. That papermakes astrongerassumptionabout theinformation contentof thepolicy announcement by assuming that the direct policy signal that can be extracted from the policy action and the statement extends out to a year. Clearly, there is room for more research to understand the horizon of the monetary policy signal, in which dimensions monetary policy surprises differ, and what effects these different surprises have on financial markets. 5 Conclusions Market-based measures of monetary policy expectations and surprises are useful because these can be calculated at high frequencies and are free of the often implausible assumptions of VAR based exercises when responses of asset prices are concerned. A favorite instrument for these measures is the federal funds futures contract. This paper demonstrated the usefulness of these contracts beyond their use in calculating the unanticipated component of the current target rate decision. The federal funds futures market is liquid out to at 21

least six months, and given the knowledge of the dates of future FOMC meetings, expectations and changes in expectations due to policy announcements can be calculated at different FOMC meeting horizons, which are the relevant intervals for interest rate changes. The first part of this paper showed the mechanics of extracting information from the prices of federal funds futures contracts. The second part used these market-based changes in expected funds rates after several FOMC meetings to help think about monetary policy as a multi-dimensional process. Rather than estimating the asset price responses to the “average” policy surprise, unanticipated policy actions are decomposed into timing, level, and slope surprises. The estimated asset price reactions to these surprise components differ significantly. While timing surprises have little effect beyond short-maturity yields, the responses to the level component suggest that the effect of a lasting policy surprise (one that actually changes expectations of funds rates for longer than an intermeeting period) are large—and these effects are understated when the “unexpected current policy action” measure of policy surprises is used. Lastly, the slope surprise has a large influence on longer term yields, perhaps because theseareperceivedtobeinformativeaboutthecentralbank’seconomicoutlook. The timing, level, and slope decomposition carried out in this paper was a purelyempiricalexercise. Aninterestingavenueforresearchwouldbetomodel the monetary policy process as consisting of more than one type of surprise, and to investigate the theoretical implications. This would tie into the role of commitment in monetary policy and differences between committing to an interest rate path rather than to an outcome, such as a level of inflation. Of course, there is significant scope for more empirical work as well. The applied exercise in this paper used only part of what can be learned from federal funds futures contracts. Further research utilizing information embedded in these 22

instrumentswillhelpinbetterunderstandinghowmonetarypolicyandfinancial markets interact. 23

References [1] Bernanke, Ben and Kenneth Kuttner (2005). “What Explains the Stock Market’s Reaction to Federal Reserve Policy?” Journal of Finance, forthcoming. [2] Cook, Timothy and Thomas Hahn (1989). “The Effect of Changes in the Federal Funds Rate Target on Market Interest Rates in 1970s,” Journal of Monetary Economics 24, 331-51. [3] Craine, Roger and Vance Martin (2004). “Monetary Policy Shocks and Security Market Responses,” working paper, University of California at Berkeley. [4] Durham, Benson (2003), “Estimates of the Term Premium on Near-dated FederalFundsFuturesContracts,”FederalReserveBoardFinanceandEconomics Discussion Series 2003-19. [5] Ellingsen, Tore and Ulf Söderström (2001). “Monetary Policy and Market Interest Rates,” American Economic Review 91, 1594-1607. [6] Ellingsen,ToreandUlfSöderström(2003).“MonetaryPolicyandtheBond Market,” working paper, Bocconi University. [7] Gürkaynak, Refet, Brian Sack, and Eric Swanson (2002). “Market-Based Measures of Monetary Policy Expectations,” Federal Reserve Board Finance and Economics Discussion Series 2002-40. [8] Gürkaynak,Refet,BrianSack,andEricSwanson(2005a).“TheSensitivity ofLong-TermInterestRatestoEconomicNews: EvidenceandImplications for Macroeconomic Models,” American Economic Review 95, 425-36. [9] Gürkaynak, Refet, Brian Sack, and Eric Swanson (2005b). “Do Actions Speak Louder Than Words? The Response of Asset Prices to Monetary Policy Actions and Statements,” International Journal of Central Banking 1, 55-93. [10] Hamilton, James and Oscar Jorda (2002). “A Model of the Federal Funds Rate Target,” Journal of Political Economy 110, 1135-67. [11] Krueger, Joel and Kenneth Kuttner (1996). “The Fed Funds Futures Rate as a Predictor of Federal Reserve Policy,” Journal of Futures Markets 16, 865-879. [12] Kuttner, Kenneth (2001). “Monetary Policy Surprises and Interest Rates: Evidence from the Fed Funds Futures,” Journal of Monetary Economics 47, 523-44. [13] Piazzesi, Monika and Eric Swanson (2004). “Futures Rates as Risk- AdjustedForecastsofMonetaryPolicy,”NBERWorkingPaperNo.10547. 24

[14] Rigobon,RobertoandBrianSack(2002).“TheImpactofMonetaryPolicy on Asset Prices,” NBER Working Paper No. 8794. [15] Rudebusch, Glenn (1998). “Do Measures of Monetary Policy in a VAR Make Sense?” International Economic Review 39, 907-931. [16] Sack, Brian (2004). “Extracting the Expected Path of Monetary Policy From Futures Rates,” Journal of Futures Markets 24, 733-54. [17] Söderström, Ulf (2001). “Predicting Monetary Policy with Federal Funds Futures Prices,” Journal of Futures Markets 21, 377-91. 25

Table 1.A: Generating the timing component Dependent Constant Level R2 Variable (std err) (std err) e0 -0.001 0.859 0.49 (0.005) (0.121) Note. Number of observations is 119. Heteroskedasticity consistent standard errors are reported in parentheses. Coefficients in bold are significant at 5%. Table 1.B: Response of asset prices to timing and level factors Dependent Constant e0 R2 Constant Timing R2 Constant Timing Level R2 Variable (std err) (std err) (std err) (std err) (std err) (std err) (std err) 3-month -0.006 0.564 0.80 -0.014 0.479 0.29 -0.005 0.479 0.562 0.82 (0.002) (0.040) (0.005) (0.061) (0.003) (0.064) (0.068) 6-month -0.005 0.563 0.64 -0.013 0.393 0.16 -0.003 0.393 0.637 0.70 (0.003) (0.050) (0.006) (0.064) (0.003) (0.060) (0.089) 2-year -0.002 0.528 0.46 -0.010 0.284 0.07 0.001 0.284 0.676 0.56 (0.004) (0.064) (0.006) (0.089) (0.004) (0.094) (0.088) 5-year 0.000 0.333 0.26 -0.005 0.151 0.03 0.002 0.151 0.452 0.35 (0.004) (0.059) (0.005) (0.790) (0.004) (0.080) (0.091) 10-year -0.001 0.170 0.13 -0.004 0.050 0.01 0.000 0.050 0.256 0.20 (0.003) (0.051) (0.004) (0.067) (0.003) (0.067) (0.081) S&P 500 -0.099 -2.930 0.24 -0.057 -1.500 0.03 -0.118 -1.500 -3.813 0.30 (0.037) (0.889) (0.049) (0.964) (0.037) (0.970) (1.018) Note. Number of observations is 119. Heteroskedasticity consistent standard errors are reported for e0 regressions. Bootstrap standard errors, as explained in text, are reported for regressions using timing. R2 statistics refer to OLS goodness-of-fit measures. Coefficients in bold are significant at 5%.

Table 2.A: Generating the timing component (post-1994) Dependent Constant Level R2 Variable (std err) (std err) e0 0.001 0.814 0.47 (0.006) (0.136) Note. Number of observations is 91. Heteroskedasticity consistent standard errors are reported in parentheses. Coefficients in bold are significant at 5%. Table 2.B: Response of asset prices to timing and level factors (post-1994) Dependent Constant e0 R2 Constant Timing R2 Constant Timing Level R2 Variable (std err) (std err) (std err) (std err) (std err) (std err) (std err) 3-month -0.006 0.594 0.80 -0.012 0.523 0.33 -0.004 0.523 0.549 0.81 (0.003) (0.050) (0.006) (0.076) (0.004) (0.077) (0.094) 6-month -0.006 0.578 0.64 -0.012 0.396 0.16 -0.003 0.396 0.640 0.72 (0.004) (0.065) (0.006) (0.086) (0.004) (0.085) (0.113) 2-year -0.002 0.506 0.37 -0.007 0.240 0.04 0.002 0.240 0.660 0.49 (0.006) (0.081) (0.007) (0.116) (0.005) (0.118) (0.115) 5-year 0.000 0.301 0.18 -0.002 0.092 0.01 0.003 0.092 0.441 0.28 (0.006) (0.074) (0.006) (0.104) (0.005) (0.108) (0.129) 10-year -0.001 0.158 0.09 -0.002 0.017 0.00 0.001 0.017 0.260 0.16 (0.004) (0.069) (0.005) (0.094) (0.004) (0.090) (0.124) S&P 500 -0.127 -3.648 0.28 -0.091 -1.873 0.04 -0.154 -1.873 -4.628 0.36 (0.048) (0.991) (0.060) (1.145) (0.045) (1.164) (1.389) Note. Number of observations is 91. Heteroskedasticity consistent standard errors are reported for e0 regressions. Bootstrap standard errors, as explained in text, are reported for regressions using timing and level. R2 statistics refer to OLS goodness-of-fit measures. Coefficients in bold are significant at 5%.

Table 3.A: Generating the timing and slope components (post-1998) Dependent Constant Level R2 Constant Timing Level R2 Variable (std err) (std err) (std err) (std err) (std err) e0 0.001 0.845 0.68 (0.005) (0.140) e2 -0.001 0.224 0.840 0.81 (0.004) (0.153) (0.088) Notes. Number of observations is 58. Heteroskedasticity consistent standard errors are reported for the first regression. Bootstrap standard errors, as explained in text, are reported for the second regression. R2 statistics refer to OLS goodness-of-fit measures. Coefficients in bold are significant at 5%.

Table 3.B: Response of asset prices to timing, level, and slope factors (post-1998) Dependent Constant e0 R2 Constant Timing R2 Constant Timing Level R2 Constant Timing Level Slope R2 Variable (std err) (std err) (std err) (std err) (std err) (std err) (std err) (std err) (std err) (std err) (std err) 3-month -0.008 0.593 0.88 -0.015 0.505 0.19 -0.007 0.505 0.536 0.89 -0.007 0.505 0.536 0.165 0.90 (0.002) (0.050) (0.007) (0.076) (0.003) (0.074) (0.109) (0.003) (0.076) (0.104) (0.079) 6-month -0.009 0.598 0.71 -0.016 0.351 0.06 -0.008 0.351 0.603 0.76 -0.008 0.351 0.603 0.377 0.81 (0.004) (0.073) (0.008) (0.127) (0.004) (0.131) (0.125) (0.004) (0.127) (0.121) (0.154) 2-year 0.008 0.550 0.38 -0.011 0.096 0.00 -0.002 0.096 0.643 0.50 -0.002 0.096 0.643 0.957 0.69 (0.007) (0.087) (0.010) (0.210) (0.007) (0.219) (0.125) (0.007) (0.221) (0.127) (0.219) 5-year 0.001 0.317 0.17 -0.003 -0.009 0.00 0.003 -0.009 0.397 0.26 0.002 -0.009 0.397 0.806 0.45 (0.007) (0.088) (0.008) (0.189) (0.007) (0.182) (0.122) (0.007) (0.186) (0.123) (0.234) 10-year 0.000 0.180 0.10 -0.003 0.021 0.00 0.001 0.021 0.215 0.14 0.001 0.021 0.215 0.600 0.32 (0.006) (0.091) (0.006) (0.149) (0.006) (0.144) (0.122) (0.006) (0.143) (0.114) (0.211) S&P 500 -0.156 -4.865 0.36 -0.093 -3.252 0.03 -0.163 -3.252 -4.746 0.38 -0.163 -3.252 -4.746 -4.537 0.43 (0.065) (1.159) (0.086) (3.005) (0.065) (3.033) (1.646) (0.067) (2.974) (1.694) (2.536) Notes. Number of observations is 58. Heteroskedasticity consistent standard errors are reported for e0 regressions. Bootstrap standard errors, as explained in text, are reported for regressions using timing and level. R2 statistics refer to OLS goodness-of-fit measures. Coefficients in bold are significant at 5%.

Figure 1 Expected Federal Funds Rates Based on Federal Funds Futures Percentage 2.00 August 13, 2002 August 12, 2002 1.75 1.75 1.69 1.56 1.52 1.50 1.50 1.46 1.45 1.40 1.25 Aug 13 Sep 24 Nov 6 Dec 10

Figure 2a Current Policy Surprise (e0) Figure 2b Timing Surprise

Figure 2c Level Surprise Figure 2d Slope Surprise