Positive feedback trading under stress: Evidence from the US Treasury securities market

Transcription

1 Postve feedback tradng under stress: Evdence from the US Treasury securtes market Frst draft: October 2001 Ths draft: May 2003 Benjamn H Cohen Internatonal Monetary Fund Independent Evaluaton Offce 1776 G Street, NW Washngton, DC 20431, USA bcohen@mf.org Hyun Song Shn London School of Economcs Houghton Street London, WC2A 2AE, UK h.s.shn@lse.ac.uk Abstract: A vector autoregresson s estmated on tck-by-tck data for quote-changes and sgned trades of 2-year, 5-year and -year on-the-run US Treasury notes. Confrmng the results found by Hasbrouck (1991) and others for the stock market, sgned order flow tends to exert a strong effect on prces. More nterestngly, however, there s often a strong effect n the opposte drecton, partcularly at tmes of volatle tradng. Prce declnes elct sales and prce ncreases elct purchases. An examnaton of tck-by-tck tradng on an especally volatle day confrms ths fndng. At least n the US Treasury market, trades and prce movements appear lkely to exhbt postve feedback at short horzons, partcularly durng perods of market stress. Ths suggests that the standard analytcal approach to the mcrostructure of fnancal markets, whch focuses on the ways n whch the nformaton possessed by nformed traders becomes ncorporated nto market prces through order flow, should be complemented by an account of how prce changes affect tradng decsons. Acknowledgments: We are grateful to Marvn Barth, Mchael Flemng, Jon Danelsson, Crag Furfne, Alan Malz, Paolo Pasquarello, Rchard Payne and El Remolona, as well as to semnar partcpants at the BIS, the LSE, the 2002 Central Bank Research Conference on Rsk Management and Systemc Rsk n Basel, the 2002 ECB Captal Markets Research Conference, and the 2003 Amercan Fnance Assocaton meetngs, for comments and dscussons on earler drafts. We are also grateful to Gert Schnabel for research assstance. All errors, and any opnons that we mght express, are our own.

2 1. Introducton A prncpal concluson of the theoretcal lterature on market mcrostructure holds that order flow the sequental arrval of the buy and sell decsons of actve traders plays a vtal role n prce dscovery. In the most nfluental papers, such as Glosten and Mlgrom (1985) and Kyle (1985), order flow plays ths role because of the presence of nformaton asymmetres, resultng n adverse selecton effects. In Glosten and Mlgrom (1985), for example, market makers do not know whether an ncomng order s from an nformed or an unnformed trader, and quoted bd and ask prces reflect a trade-off between losses to tradng wth nformed traders and profts to tradng wth unnformed traders. By means of a vector autoregresson (VAR) analyss of the tme seres propertes of equty prce changes and order flows, Hasbrouck (1991) documents a number of apparently robust emprcal fndngs. Notably, order flow nfluences prces n the way predcted by the theory. Buy orders rase prces and sell orders lower prces, and there s a component of the prce change that may be regarded as the permanent prce mpact of a trade that remans even after tme has elapsed to smooth away transtory effects. Evans and Lyons (2002) document smlar fndngs for the foregn exchange market. Another robust fndng n Hasbrouck s study, however and one whch s relevant for our paper s that there s also a strong relatonshp n the opposte drecton: from prce changes to order flows. Specfcally, Hasbrouck fnds a strongly negatve relatonshp between current order flow and past prce changes. In other words, prce ncreases are followed by sales, and prce falls are followed by purchases. Expressed n tabular form, ths relatonshp corresponds to the top rght cell of the followng matrx of relatonshps between prce changes and sgned trades. 2

3 Endogenous varables Return Sgned Trade Explanatory Varables Past returns Past sgned trades + + Gven the strong postve effect of past order flow on prces, the negatve relatonshp between returns and subsequent order flow therefore has a mldly dampenng effect on prce behavour. We take the VAR methods used by Hasbrouck (1991) and apply them to hgh frequency data on the U.S. treasury securtes market. Our conclusons pont to some nterestng and revealng dfferences from Hasbrouck s orgnal results for the stock market. We fnd that under tranqul market condtons, when tradng s orderly and tradng frequency s low, most of the qualtatve conclusons found n Hasbrouck s study are replcated. However, durng perods of actve tradng and hgh prce volatlty, there appears to be a structural shft n the market dynamcs. In such perods, a prce ncrease elcts more buy orders and a prce decrease elcts more sell orders. In tabular form, the relatonshp between returns and sgned order flows take on the followng form. Endogenous varables Return Sgned Trade Explanatory Varables Past returns /? + Past sgned trades + + Compared wth Hasbrouck s study, the top rght hand cell changes sgn, and becomes postve. The negatve autocorrelaton of returns also becomes less pronounced. On 3

4 the face of t, there s some evdence of postve feedback tradng n whch order flow tends to magnfy recent returns. We llustrate these general fndngs by examnng n some detal the partcularly volatle tradng on February 3 rd 2000, when markets were unsettled followng the U.S. Treasury s announcements on debt management polcy and rumours about large losses at certan nsttutons. Postve feedback tradng n low frequency data (weekly or monthly) s often assocated wth momentum tradng and other explanatons that appeal to boundedly ratonal traders (De Long et al. (1990), Jagadeesh and Ttman (1995), Grnblatt, Ttman and Wermers (1995)). Our focus s very dfferent. At the level of tck-by-tck data, such as n our study, postve feedback tradng hghlghts the ncentves of sophstcated traders that operate under pressurzed tradng condtons, n whch they are acutely aware of the actons of other traders n the market. For example, postve feedback tradng may result f a sgnfcant number of market partcpants are constraned (and know one another to be constraned) n ther actons by nsttutonally mandated loss lmts. For a trader who s close to breachng hs loss lmt, an adverse prce move may force hm to lqudate hs tradng poston. If there are other traders who have smlar tradng postons, there wll be spllover effects n whch the lqudatons of one trader pushes prces adversely for other traders. The effect of the loss lmt s to shorten the decson horzon of the traders. Irrespectve of what a trader beleves about the fundamental value of the asset beng traded, the constrants mposed by loss lmts, or by smlar mechansms such as margn calls or (n extreme cases) bankruptcy constrants, wll dctate a course of acton n certan crcumstances. Thus, one way of understandng feedback tradng at hgh frequency s n terms of the constrants on traders that shorten ther decson horzons and thereby encourage mutually renforcng behavour. In partcular, f some traders beleve that others wll be faced by such constrants, they may attempt to antcpate the results of a sharp prce move or magnfy the tradng proft of rdng short term prce trends by sellng nto a fallng market or buyng nto a rsng one. Postve feedback tradng s consstent wth the market adage that one should not try to catch a fallng knfe that s, one should not trade aganst a strong trend n prce. Some recent studes are also consstent wth such behavour. Hasbrouck (2000) fnds 4

5 that a flow of new market orders for a stock are accompaned by the wthdrawal of lmt orders on the opposte sde. Danelsson and Payne s (2001) study of foregn exchange tradng on the Reuters 2000 tradng system shows how the demand or supply curve dsappears from the market when the prce s movng aganst t, only to reappear when the market has reganed composure. Evans and Lyons (2003) fnd that exchange rates do not adjust mmedately to the publc announcements of macroeconomc news, but rather that there s an nteracton between the ntal prce change and subsequent order flow whch pushes prces to ts eventual new level. Theoretcal models of such behavour are stll n ther nfancy, but the recent lterature on endogenous lqudty has attempted to address the short term ncentves that operate n an actve market wth strategc traders. Bernardo and Welch (2002) argue that lmted lqudty can nfluence the tradng decsons of traders. Brunnermeer and Pedersen (2002) show how the potental dstressed sellng of small traders can be exploted by a large trader to manpulate the prce. In Morrs and Shn (2003), traders wth short horzons and prvately known tradng lmts nteract n a market for a rsky asset. Rsk-averse, long horzon traders supply a downward slopng resdual demand curve that face the short-horzon traders. When the prce falls close to the tradng lmts of the short horzon traders, sellng of the rsky asset by any trader ncreases the ncentves for others to sell. Sales become strategc complements between the short term traders, and payoffs analogous to a bank run are generated. In the analogue of the run outcome n a bank run model, short horzon traders sell because others sell. Usng global game technques, Morrs and Shn solve for the unque trgger pont at whch the lqudty black hole comes nto exstence. Recent emprcal studes of the mpact of lqudty on asset prces such as Kambhu and Mosser (2001), Acharya and Pedersen (2002) and Pastor and Stambaugh (2002) pont to the mportance of constrants on short term tradng strateges and ther mpact on asset prces. Provdng a theoretcal bass for postve feedback tradng s an mportant but (as yet) unresolved task, although the recent lterature has made some headway. Our emprcal results are not ted to any partcular theoretcal model, and can be read ndependently of any presumed story of feedback tradng. We ntend ths study as the frst step towards a more systematc nvestgaton of the nteracton between market dynamcs and tradng strateges at the hgh frequency level. 5

6 The next secton descrbes the dataset used and apples a VAR specfcaton to ntraday tradng n on-the-run US Treasury notes over the perod Secton 3 examnes tradng on an especally volatle day n some detal, as a way of llustratng the ways n whch prce and transacton behavour can shft suddenly n volatle tradng condtons n ways that cannot be fully explaned by an approach based on adverse selecton and order flow. Secton 4 concludes. 2. Testng for strategc nteracton among traders 2.1 The data The data are provded by GovPX, Inc. GovPX provdes subscrbers wth real-tme quotes and transacton data on US Treasury and agency securtes and related nstruments compled by a group of nter-dealer brokers, ncludng all but one of the major brokers n ths market. For each ssue, GovPX records the best bd and offer quotes submtted by prmary bond dealers, the assocated quote szes, the prce and sze of the most recent trade, whether the trade was buyer- or seller-ntated, the aggregate volume traded n a gven ssue durng the day, and a tme stamp. Dealers are commtted to execute the desred trade at the prce and sze that they have quoted to the brokers. However, counterpartes can often negotate a larger trade sze than the quoted one through a work-up process. Flemng (2001), who provdes an extensve descrpton of ths data set, estmates that the trades recorded by GovPX covered about 42% of daly market volume n the frst quarter of We examne quotes and trades n two-year, fve-year and ten-year on-the-run (.e., recently ssued) Treasury notes over the perod from January 1999 to December Although GovPX provdes round-the-clock data, we restrct the seres to quotes and trades that take place between 7:00 am and 5:00 pm, when tradng s most frequent. The quotes used are the mdpont of the prevalng bd and ask quotes. When a new ssue becomes on the run, the GovPX code ndcatng on-the-run status swtches to the new ssue startng at 6:00 pm; ths means that a gven set of ntraday quotes and trades wll always refer to the same ssue. Trade volumes are calculated as the dfference n the aggregate daly volume recorded for the correspondng securty. Because these fgures are provded n chronologcal order, the result s an ordered dataset n whch each observaton s ether a quote-change, a trade or both. 6

7 Table 1a summarses the data used for the three securtes. Our observatons are n event tme rather than chronologcal tme. One ssue s whether the tck by tck returns should be normalzed so that they are comparable to calendar returns over a fxed tme nterval. Our man qualtatve results turn out to be nsenstve to whether we normalze or not. For the results to be reported below, returns (r t ) are defned as the dfference n the log of the quoted prce (more precsely, the mdpont between the prevalng bd and ask quotes) at event tmes t and t-1. The number of observatons ncreases wth maturty, whle the number and sze of transactons falls. In other words, the dataset ncludes more quote changes and fewer transactons as maturty rses. Durng the sample perod, an average of $4.6 bllon of trades are recorded daly on GovPX for the two-year note, more than the fve year ($2.5 bllon) and ten-year ($1.6 bllon) combned, reflectng both more trades and a greater volume per trade. As suggested by Flemng (2001), ths may reflect dfferences n coverage by GovPX rather than dfferences n the actual relatve lqudty of 2, 5 and year ssues, snce the excluded broker (Cantor Ftzgerald) s relatvely more actve n longer term ssues. The mean absolute value of the return from one observaton to the next rses wth maturty. 1 The same s true for daly returns. Table 1a also gves the average duraton (the tme between observatons) for the full sample of each bond and for four subsamples. Ths s about one mnute for the 2-year note, and about 45 seconds for the 5- and -year notes. For the ffty tradng days where average duraton s hghest, the tme gap s slghtly less than two mnutes for all three notes, whle for the ffty tradng days wth the lowest average duraton, ths gap s about 40 seconds for the 2-year note and 30 seconds for the 5- and - year notes. Ths suggests that, whle there clearly are more actve and less actve tradng days n the sample, dvergences n the frequency wth whch quotes and/or trades are observed are not great. Average duratons are also presented for the ffty days where the dfference between the daly hgh and low prce (the daly tradng range) for the specfed bond s hghest, and for the ffty days where ths dfference s lowest. We would expect days n the 1 In terms of 32nds, whch are the usual quote conventon for Treasury notes, and assumng a prce close to 0, the mean absolute returns shown correspond to prce changes of nds for the 2-year, nds for the 5-year, and nds for the -year note. 7

8 former sample to correspond to relatvely volatle tradng condtons, whle days n the latter are relatvely quet. Agan, a clear dfference between the two samples n terms of average duraton can be observed. Days wth wde prce swngs tended to see more frequent trades and/or quote changes, wth observatons comng n every 40 to 45 seconds, than queter days, when the tme between observatons averaged 92 seconds for the two-year note and 56 seconds for the ten-year. Duraton s also longer for lowvolatlty days (measured by the standard devaton of the tck-by-tck returns) than for hgh-volatlty days. Confrmaton of the relatonshp between the frequency of tradng and varous volatlty measures s presented n Table 1b for the 2-year note. The average duraton on a gven day tends to be negatvely correlated wth the range (hgh-low) of prces observed durng the day, and the standard devaton of tck-by-tck returns durng the day, whle the prce range and volatlty dsplay a strong postve correlaton. None of these varables seems to have a strong correlaton wth the change (open-close) n prces that occurred durng the day, suggestng that tradng condtons were about as volatle on days when bond prces rose as on days when prces fell. 2.2 Testng for the cross-effects of trades and quote revsons What mght the data tell us? GovPX records the prcng and tradng decsons of bond dealers, rather than those of speculatve traders or long-term nvestors. A reasonable assumpton s that the dealers partcpatng n the system attempt to mnmse ther open exposures to bond yelds as far as possble, and do not attempt to take a vew on lkely yeld movements. 2 Under ths assumpton, when a dealer accepts a bd or offer that has been posted on the system, he could be followng one of two possble behavoural rules. One s that, whenever the dealer executes a trade wth a customer, ether by sellng her a bond out of nventory or by buyng a bond from her, the dealer mmedately submts a countervalng trade to an nter-dealer broker n order to reman balanced. The other s that the dealer only rebalances hs exposure perodcally. Under the frst rule, a 2 Some dealers, however, execute trades on behalf of propretary tradng desks under the umbrella of the same fnancal nsttuton. For the purposes of ths dscusson, a propretary tradng desk would be thought of as a customer of ts afflated dealer. Durng the tme perod covered by ths study, January 1999-December 2000, many of the major government bond dealers had ether closed or serously curtaled ther propretary tradng operatons. 8

9 transacton observed n the GovPX data closely tracks the transacton decson of a poston-taker n the market. Under the second, an observed transacton prmarly reflects nventory control operatons and not a poston-takng decson, except n the sense that a seres of poston changes should eventually (after several mnutes or a few hours) lead to a correspondng nventory adjustment transacton. To the extent that both of these motvatons are n acton, the dealer-submtted transactons compled by GovPX are lkely to reflect a combnaton of the speculatve strateges of traders and the nventory-control strateges of dealers. The quotes posted on the system are also lkely to reflect a combnaton of speculatve and nventory-control motves. At certan tmes, a dealer may adjust hs posted bd and ask quotes because of the nformaton that he has gleaned from customer order flow. At other tmes, he may shade posted bd and ask quotes n order to nduce a suffcent number of buy or sell orders to brng nventory back nto lne wth ts desred level. Both categores of motves are lkely to nfluence the posted quotes that we observe on GovPX. A prmary am of the analyss of ntraday fnancal market data s to understand how the mcrostructure characterstcs of a gven market affect the tme-seres characterstcs of prce quotes, sgned transactons, and the nteractons between them. If the dealers whose quotes and trades are recorded by GovPX are prmarly mmckng customer orders, then ths would allow us to test for the nformatonal nteracton between prces and trades. Specfcally, we could test the result n the theoretcal lterature on market mcrostructure noted above, namely that sgned order flow should have a measurable mpact on prce formaton. We could also test whether, for reasons that wll be dscussed n more detal n Secton 4, lagged prce movements have an mpact on tradng under certan condtons. Further, there are reasons to beleve that the tme seres of both order flow and returns themselves exhbt seral dependence. Among the factors that mght produce such dependence are nventory control motves, lagged adjustment to ncomng nformaton, and mnmum tck szes. Some of these factors would result f dealers followed a customer-drven rule, whle others would mply the prmacy of nventory adjustment n short-run dealer behavour. 9

10 At a short enough tme horzon data observed n ntervals of mnutes and seconds, rather than days or months one mght expect these factors to exert an mpact on observed quotes and trades that can be measured statstcally, even f at longer tme horzons prce changes are thought of as beng drven more or less exclusvely by the arrval of new nformaton. Examnng prces and trades over very short ntervals of tme could thus enable us to determne whch rules are beng followed by the dealers n the market and, f we thnk the mmckng of customer orders s mportant, to learn more about customer behavour as well. It should be noted that the securty prces studed n ths paper those of on-the-run US Treasury notes are n fact proxes for the underlyng values that are of nterest to traders and nvestors. Thus, a trader who buys a two-year Treasury note may be dong so as part of a strategy to adopt or modfy her exposure to some other value, such as the one-year forward rate startng one year from the present, or the spread between Treasury and mortgage-backed securtes. Smlarly, there are other ways to adopt the same exposure, for example n the futures market. By studyng the mpact of past returns and trades on present returns and trades, we are thus gnorng many other relevant varables. For example, the return on the on-the-run two-year Treasury note wll also reflect returns and trades of other Treasury securtes, futures nstruments, mortgage bonds, and even equtes and foregn exchange nstruments. The tests presented here should thus be understood as efforts to measure the strength and drecton of the effects beng tested, rather than to formulate a fully specfed model of the market for US Treasury securtes A two-varable VAR of sgned trades and returns The followng vector auto-regresson (VAR) should capture many of these shorthorzon effects: r t = trade = 1 t α r = t = 1 + γ r = 0 t β trade + = 1 t + ε δ trade t 1, t + ε 2, t (1) Here r t s the return varable cted above, whle trade t s a sgned trade varable. Two varables are used for trade t :

11 x t, an ndcator varable equallng 1 for a buyer-ntated transacton, -1 for a seller-ntated transacton, and zero where there s a change n the prce quote wthout a transacton; and v t, the sze of the trade n mllons of dollars, multpled by 1 for a buyerntated transacton and -1 for a seller-ntated transacton. The verson usng x t s essentally dentcal to the VAR computed by Hasbrouck (1991). Lke Hasbrouck we estmate the contemporaneous mpact of trades on prces. That s, we nclude a term β 0 trade t on the rght-hand sde of the frst equaton. Ths allows for the possblty that trades are observed slghtly before quote revsons, for example through the workup process. 3 Although the estmate of β 0 s postve and sgnfcant n all versons of the VAR that we examne, excludng the contemporaneous trade t from the estmaton of the frst equaton produces qualtatvely smlar results. Results from the estmaton of equaton (1) on the full two-year sample are presented n Table 2 for trade t = x t, and n Table 3 for trade t =v t. For each tradng day, the calculaton of the VAR starts wth the eleventh observaton of the day as the dependent varable. Ths elmnates the above-mentoned effect of the swtch from one on-the-run ssue to the next, the nfluence of overnght prce changes and the ncluson of the effects of the last few observatons n one day on the frst few observatons n the next. For three of the four quadrants of coeffcents the effects of lags of r t on r t ; the effects of contemporaneous and lagged trade t on r t ; and the effects of lags of trade t on trade t there s a remarkable degree of consstency across the three maturtes (2-year, 5-year and -year) and across the two trade varables (x t and v t ). The results for all three quadrants conform to those found by Hasbrouck (1991) for the US equty market. Lagged returns tend to exert a negatve effect on present returns, though ths effect s partally reversed n later lags. In other words, returns are negatvely autocorrelated at very short tme ntervals. Although we use quote mdponts to 3 In January 2000, the average length of the workup process was seconds for the on-the-run twoyear note, seconds for the fve-year note and seconds for the ten-year. These are all less 11

12 calculate r t, even for observatons where the new lne of data represents a new transacton (that s, we use the prevalng quotes rather than the transacton prce), t s possble that the negatve autocorrelaton reflects a bd-ask bounce effect as descrbed by Roll (1984). Engle and Patton s (2000) study for NYSE stocks show that the prce mpact of an order falls asymmetrcally on the bd and ask quotes. Buyer ntated trades prmarly move the ask prce whle seller-ntated trades move the bd prce. When one sde of the quote s updated more quckly than the other n response to an order, the md quote would exhbt behavour smlar to the bd-ask bounce. Current and lagged trades tend to exert a postve effect on present returns. In other words, prce movements follow order flow. Besdes Hasbrouck s fndngs for the equty market, smlar effects have been found for the Treasury market by Flemng (2001) and for the foregn exchange market by Evans and Lyons (2002). Lagged trades tend to exert a small but sgnfcantly postve effect on current trades. In other words, trades are postvely autocorrelated. Ths may suggest that traders tend to adjust ther postons n a seres of trades, rather than all at once, or that some traders respond to new nformaton wth a lag. It s n the upper rght quadrant the effect of lagged returns on current sgned trades where the consstency breaks down somewhat across maturtes, and where the results are generally dfferent from Hasbrouck s. For the 2-year and 5-year notes n the VARs usng x t, and for all three maturtes n the VARs usng v t, the coeffcents on lagged returns (sometmes wth the excepton of the frst lag) tend to be postve for current trades. In other words, prce ncreases tend to be followed by buy orders, at short horzons, whle prce decreases are followed by sell orders. Only for ten-year notes n the VARs usng x t are the coeffcents generally negatve, correspondng to Hasbrouck s results for the equty market. Ths set of effects wll be the focus of Sectons 3 and 4 of the paper Estmatng cumulatve effects A standard tool for analysng the results of VARs s the mpulse-response functon. In the present case, however, we are nterested not n the usual mpulse-response than the average tck lengths, whch were 59, 46 and 44 seconds respectvely. Bon and Leach (2001) descrbe and analyse the workup process n the US Treasury market. 12

13 functon - the effect on the level of one of the varables at some future pont from a shock to a varable n the system - but n the cumulatve effects of shocks to the ncluded varables. Thus, for example, we want to know the mpact of a new buy order on the overall return over the next several mnutes, rather than on the level of the observed return at a specfc pont n the future. Smlarly, we want to know the total number of net buys or sells that happens n the aftermath of a new buy or sell. To do ths, we can cumulate the output of the usual mpulse response functon, takng account of the presence of the contemporaneous sgned trade as an explanatory varable n the return equaton. To construct the orthogonalsed shocks to sgned trades and returns, we need to make a pror assumpton about the drecton of causalty between the varables. In ths case, we assume that sgned trades cause returns. Graphs 1 to 4 show the cumulatve effects of a one-unt ncrease n returns and buys (the x t varable) on the cumulatve return and number of net buys over the followng twenty perods for the two-, fve- and ten-year Treasury notes. The graphs largely confrm the results dentfed n our earler revew of the sgns of the respectve raw coeffcents. Roughly 77% of a gven shock to the return of the fve-year note s stll contaned n the prce level 20 perods later; ths proporton falls to 69% for the two-year and 68% for the ten-year note (Graph 1). A buy order has a strong postve effect on returns n the short term; a buy causes a cumulatve postve return of about 0.27 hundredth of a percent for the two-year note, 0.63 hundredths of a percent for the 5-year note, and 1.05 hundredths of a percent for the -year note (Graph 2). In the twenty observatons after a net buy order s recorded, a further 0.74 net buys result for the 2-year note, 0.60 net buys for the 5-year, and 0.38 for the - year (Graph 4). As maturty ncreases, there seems to be a greater mpact of trades on returns and less postve autocorrelaton of trades. One possble explanaton of ths s the relatvely lower fracton of the market covered by the data at hgher maturtes. It s lkely that returns are nfluenced not only by the trades executed by the brokers partcpatng n GovPX, but also by those executed by the excluded broker; hence the mpact of a trade on the observed return s overestmated when one looks only at GovPX trades. Smlarly, the autocorrelaton of trades s underestmated, because one s lookng only 13

14 at a fracton of the actual trades n any gven perod of tme. There do not appear to be strong dfferences across maturtes n the pattern of autocorrelaton n returns. The cumulatve mpact of returns on trades, whch as already noted dffers strkngly from Hasbrouck s results, s llustrated n Graph 3. The graph shows the mpact of a one-unt ncrease n the return. When one consders the typcal sze of these returns, t becomes clear that the magntude of the effect s not large. For the two year note, for example, an ncrease of one standard devaton n the return (a return of 4.46 x -5 from one tck to the next, or about 0.4 hundredths of a percentage pont) leads to the occurrence of 3.7% more net buys than would otherwse take place over the subsequent twenty perods, or roughly 19.6 mnutes. 4 For the fve-year note, there are 3.5% more net buys when the return rses by one standard devaton. However, the fact that the coeffcents from the underlyng VARs are sgnfcant suggests that ths s more than a statstcal artefact. For the ten year note, the cumulatve effect on x t s negatve, wth net buys fallng by 1.5%. 2.3 Estmaton results for duraton-based subsamples More nterestng than the sze of these effects s the way they change over dfferent subsamples. The lnes n Table 4 labelled Low duraton show the effects estmated from a VAR smlar to that n equaton (1) for the days on whch the average adjusted duraton s unusually low. These should be the days of relatvely hectc tradng (and ndeed, as already noted, prce volatlty and the dfferental between the daly hgh and low tend to be hghest on these days). Smlarly, the Hgh duraton lnes show the estmated cumulatve effects on days when average adjusted duraton was unusually hgh. These should be days when tradng and changes n quotes are relatvely slow, suggestng quet tradng condtons. More precsely, the tables show the sums of dfferent combnatons of coeffcents from the followng VAR 5 : 4 More precsely, the fracton of total transactons n the next twenty perods that are buys s hgher than t otherwse would have been. 5 To save space, the coeffcents from ths and the other VARs n the remander of the paper are not gven. Coeffcents from these VARs are avalable from the authors. 14

15 r t x t = = = 1 = 1 ( α + α d L ( γ + γ d L L t- L t - + α d H + γ d H H t - H t - ) r ) r t t + + = 0 = 1 ( β + β d L ( δ + δ d L L t - L t- + β d H H + δ d H t- H t- ) x ) x t t + ε + ε 1, t 2, t (2) The dummy varable d L t takes the value of one when an observaton occurred on one of the ffty days (% of the sample) when duraton, adjusted for tme-of-day, seasonal, and tme trend factors, was at ts lowest, whle d H t s one for observatons on the ffty days when adjusted duraton was hghest. Table 4 also gves the sgnfcance levels for dfferent combnatons of varables, usng a Wald test for the hypothess that ths sum s dfferent from zero. The duraton-based subsamples are determned usng an adjusted measure of duraton. Ths adjusted duraton equals the rato of the actual duraton to the ftted values from a model that estmates duraton usng tme-of-day, tme-of-year, and trend effects. The model closely resembles the lnear splne model wth nodes at the top of each hour developed n Engle (2000). We nclude a tme trend n the estmaton n order to account for the fact that the number of observatons tends to declne throughout the sample perod, reflectng the steadly declnng share of US Treasury market tradng that s covered by the data. We also add dummy varables for observatons n November and December, two months when these markets are less actve. The result s a seres of ftted duraton estmates for each Treasury note studed. The values of these ftted estmates, when graphed over the tradng day, exhbt a dstnct U - shape (Graph 5). Actvty s very slow between 7:00 and 8:00 am, then speeds up dramatcally between 8:00 and 9:00, when the most closely watched economc statstcs tend to be released. The market then slows somewhat, but remans actve untl 3:00 pm, after whch transactons and quote changes dwndle. Adjustng duraton by dvdng t by these ftted values results n a tme seres of duraton surprses. For all three maturtes, the effects of trades on returns tend to be hgher on the lowduraton days than on the hgh-duraton days or on the days when duraton was nether unusually hgh nor unusually low. These effects do not change n a sgnfcant way, however, when one compares unusually hgh-duraton days to normal days. Ths suggests the structural change may be non-lnear: low-duraton days stand out but hgh-duraton days do not. 15

16 Effects n the opposte drecton from returns to subsequent tradng behavour also shft on hgh- and low-duraton days relatve to the rest of the sample. For the 2-year note, these effects are more strongly postve on low-duraton days than n normal tmes (that s, they lead to more net buys), though the Wald test does not support the hypothess that ths change n the varables s sgnfcant. On hgh-duraton days, however, the effects become nsgnfcant n a statstcal sense, and a Wald test supports structural change at an 8% sgnfcance level. For the 5-year note, the results are qualtatvely smlar: there s no statstcal dfference between effects on lowduraton and normal days, whle the effects become nsgnfcant on hgh-duraton days. For the -year note, t wll be recalled that postve prce movements cause an ncrease n net sellng n the sample as a whole. These effects, as well, become nsgnfcant on hgh-duraton days. Impulse response functons for the dfferent subsamples are llustrated for the twoyear note n Graphs 6a-6d. For the cross-effects of sgned trades on returns and returns on sgned trades, these confrm what was observed from lookng at the raw coeffcents n Table 4. Whereas a new buy leads to an ncrease of 0.27 hundredths of a percent n the cumulatve return after twenty perods n the sample as a whole, on low-duraton days the mpact rses to 0.40 hundredths of a percent, whle on hghduraton days t falls to 0.23 hundredths of a percent (Graph 6b). Effects n the opposte drecton grow stronger as well. For the sample as a whole, t wll be recalled that an addtonal standard devaton return results n an ncrease of 3.7% n the number of buy orders n the next twenty perods. On low-duraton days, ths rses to 5.3%, whle on hgh-duraton days net buys declne by 0.7% (Graph 6c). Ths ncrease n the mutual mpact of trades and returns on one another results n an ncrease n the persstence of shocks to returns. For the full sample, 69% of a shock to the quote mdpont remans n the prce after twenty perods. On low duraton days, ths proporton rses to 86%, whle on hgh-duraton days t falls to 62% (Graph 6a). However, the mpact of a new trade on the drecton of tradng does not change apprecably across the dfferent subsamples (Graph 6d). 16

17 3. A case study: February 3, 2000 The results n Secton 2 suggest that, on days of relatvely rapd tradng actvty, traders tend to renforce prce movements (at least at short tme horzons) rather than dampenng them. Ths secton explores the dynamcs of ths shft on a very volatle tradng day that occurred durng the sample perod. 3.1 Events of February 3 February 3, 2000, wtnessed the sxth hghest daly tradng range for the on-the-run two-year note n the sample perod (Graph 7). The prce quoted on GovPX (usng the average of the prevalng bd and ask quotes) for the two year note opened at at 7:04 am, reached a low of at :03 am, rose to a hgh of nearly at 12:36 pm, and fnshed at at 5:00 pm. The range of the prce from ts lowest to ts hghest pont, 0.45% of par, s very large n comparson wth the sample medan daly prce range of 0.12%, the mean absolute value of the daly prce change (open to close), 0.07%, and the standard devaton of the daly prce change, 0.09%. Ths prce range corresponds to 85 bass ponts n yeld, n comparson wth a medan daly yeld range of 23 bass ponts. News accounts of the tradng on February 3, a Thursday, do not pont to a specfc new pece of macroeconomc nformaton beng dgested by the market. The market was reported to be unsettled by the US Treasury s plans to change ts aucton practces and repurchase selected ssues as part of a broader polcy of usng budget surpluses to reduce the debt held by the publc. A key pece of publc nformaton relevant to that polcy had been released on February 2, when the Treasury outlned plans to reduce the amounts of specfc maturtes to be ssued n future auctons, ncludng the popular 30-year bond. Ths announcement came durng tradng hours on the 2 nd, so t was no longer fresh news to the market on the 3 rd. Nevertheless, market commentary relatng to tradng on the 3rd focused on the uncertan envronment created by the prevous day s announcement. In ts daly report on the US Treasury market, the Assocated Press emphassed the uncertan mplcatons of the new Treasury program on the lqudty of the 30-year bond, and the effects ths uncertanty had had on market tradng. Accordng to one fund manager: Folks are knd of shocked. Treasures have become a scarce commodty. It s wld, wld stuff, as Johnny Carson used to say. It s defntely a 17

18 new envronment for everybody. We re all tryng to fgure out what ths means for the future (AP Onlne, 2000). In the same artcle, the Assocated Press noted another seres of events whch may have nfluenced tradng on February 3: Addng to Thursday s mayhem was a wdespread rumor that the dramatc declne n bond yelds had wped out a large unnamed fnancal nsttuton and that a rescue meetng was beng held at the Federal Reserve Bank of New York. The rumor prompted a statement from the New York Fed denyng there was a meetng to dscuss market volatlty (AP Onlne, 2000). An tem released on the Market News Internatonal Wre at 12:14 pm on that day reads n ts entrety: NEW YORK (MktNews) - A spokesman for the Federal Reserve Bank of New York Thursday declned all comment on a rumor wdespread n fnancal markets that there would be an emergency meetng at the Fed to address bg losses at a fnancal frm. The spokesman sad t s Fed polcy not to comment on such rumors. The completely unsubstantated rumor crculated all mornng Thursday, and appeared related to the market dslocatons trggered by the Treasury's plans to cut back on supply of long-term securtes. That has resulted n an nverson n the Treasury yeld curve n recent days and a huge rally n Treasury long bonds Wednesday and Thursday. 6 February 3 thus seems to offer an excellent opportunty for a case study of patterns of tradng n the US treasury market under condtons of uncertanty. Wth the excepton of the Fed s announcement denyng the rumour, there was no occason when a pece of prce-relevant nformaton smultaneously became known to all partcpants. Instead, there was uncertanty as to how markets themselves would be expected to behave n the new envronment of shrnkng supply. The rumours of an nsttuton n trouble added to the uncertanty, but undoubtedly, as tends to happen n these stuatons, the man area of uncertanty for market partcpants was the nature and extent of the knowledge possessed by other partcpants. 6 We are grateful to Mchael Flemng for callng our attenton to ths news story. 18

19 Examnaton of Graph 7 suggests that the day can be dvded nto four perods n terms of tradng behavour. Characterstcs of these perods, and comparable fgures for the full two-year sample, are presented n Table 5. From 7:00 am to 11:00 am, prces were flat or slghtly hgher, bd-ask spreads were wder than usual but steady, duraton was somewhat shorter than usual, and there was a roughly even balance between buys and sells. From 11:00 am to 12:15 pm, prces rse sharply, accompaned by an mbalance of buys over sells and a shortenng of duraton. Ths s presumably the tme when rumours about a troubled nsttuton domnate market tradng, wth prces at frst bd up on the expectaton that the nsttuton would have to close out a large short poston. From 12:15 pm to 2:00 pm prces fall about as sharply, wth sells outnumberng buys and duraton remanng very low. Ths followed the New York Fed announcement. In both the second and thrd perods, quoted bd-ask spreads are wde and volatle, and occasonally negatve. 7 Fnally, from 2:00 pm to 5:00 pm, prces rse gradually amd relatvely calm condtons, wth duraton close to normal levels, though bd-ask spreads reman elevated. Two ponts are worth notng wth regard to Table 5, both of whch suggest that the bond market on February 3 behaved n a more complex way than would be mpled by a smple adverse selecton model n whch nformaton s ncorporated n order flow. Frst, whle t s clear that an mbalance of buy orders over sell orders was assocated wth rsng prces and vce versa, t s nterestng that a vrtually dentcal share of buys (66%) led to a sharp prce ncrease between 11:00 and 12:15, but to only a relatvely mld prce ncrease between 2:00 and 5:00. Second, the bd-ask spread was at ts hghest between 12:15 and 2:00 - even though, as noted above, the Fed announcement was probably the day s most nfluental pece of publc nformaton. If wde bd-ask spreads ndcate a hgh degree of nformaton asymmetry, as the adverse selecton model would predct, one would expect that when an mportant tem of news, wth a drect and mmedate bearng on market prces, becomes known smultaneously to all market partcpants, ths would contrbute to a sgnfcant narrowng of bd-ask spreads. 7 Both the very wde and the negatve bd-ask spreads are probably the result of stale quotes that dealers dd not have tme to update. 19

20 3.2 Prce movements and order arrval: A closer look A closer examnaton of tradng patterns throughout the day presents further puzzles (Graphs 8a - 8d). It s worthwhle, frst, to consder what the dfferent theoretcal frameworks used n market mcrostructure would predct about the patterns of prce movements and orders. A pure neoclasscal vew would suggest that the prce moves automatcally to adjust to new nformaton, and that buys and sells should be essentally balanced whatever the prce level s and n whatever drecton t s movng. If orders prmarly reflect nventory adjustment, then groups of buys and sells should alternate, wth a large number of buys leadng to prce ncreases (as dealers rebuld nventory) and sells leadng to prce decreases (as they lay off nventory) n an essentally predctable rhythm. Accordng to an adverse selecton-based vew, we would expect to see an exogenous buldup of purchases to be followed more or less mmedately by nformaton-drven prce ncreases, and a buldup of sales to be followed by prce declnes. Durng the 7-11:30 perod (Graph 8a), buys and sells appear to be balanced over the perod as a whole, but do not seem to follow any of these predctons closely. Rsng prces are assocated wth buys (e.g. just after :04) and declnes wth sells (e.g. just before 8:18). But the order flows and prce movements appear to be smultaneous; the prce graph does not wat for a buldup of orders before t starts movng. And perods of persstent one-sdedness n the market (e.g. the buyng actvty from :17 untl around :40) are not followed by prce movements that would be sustaned enough to return nventores to balance; nstead, on ths occason, the prce hovers for a whle, then turns downward - and only then (around :44) do we see clusters of sales. As the rumours of a troubled nsttuton begn to take hold (Graph 8b), the prce rses amd heavy buyng. But sometmes the prce rses wth lttle or no buyng, as n the phase just after 11:46, and agan around 12:12. At the very top of the market, from around 12:15 onward, traders appear to be buyng at peaks, and sellng at valleys. Agan, nether the neoclasscal, nor the nventory adjustment, nor the adverse selecton vew appears to explan the nteracton between prce and order behavour. The perod after the Fed announcement (Graph 8c) s vrtually the mrror mage of the hour or so that preceded t - ths despte the very dfferent nature of the nformaton that was drvng the market n the two perods, wth rumours replaced by credbly stated facts. Prces sometmes fall wthout any order flows, other tmes assocated 20

21 wth heavy sellng. Prces seem to stablse around 1:05 pm, even though traders contnue to sell. A cluster of buys eventually emerges just before 1:16, but the market seems happy wth ts new level - even when the buys are followed by further sales. Durng the last three hours of the tradng day, the market rses slowly and wthout much volatlty (Graph 8d). A heavy seres of buy orders does not do much to move the prce. These may derve from traders coverng short postons entered nto durng the prevous phase, or they may represent the rebuldng of nventory by dealers (though an examnaton of cumulatve order flow, not shown here, would cast doubt on ths). For an example of an alternatve knd of prce volatlty, consder the tradng pattern for the 2-year note on the mornng of January 28, 2000 (Graph 9). In ths case new nformaton an unexpectedly strong non-farm payroll fgure became nstantaneously avalable to vrtually all market partcpants when the data were released at 8:30. Tradng appears to have reflected frst the antcpaton of, then the accommodaton to, ths new nformaton, whle vrtually no trades took place when the announcement was beng made. Whle some poston-takng n antcpaton of the announcement moved the prce somewhat, n the aftermath of the announcement trades tend to have lttle or no mpact on the prce, perhaps because partcpants understand that ths represented the squarng of speculatve postons and the rebalancng of portfolos. Tradng volume s much hgher after the announcement than before, as can be seen n the shorter tme ntervals between the tmes ndcated on the x-axs (whch are spaced 50 tcks apart). Ths pattern of the adjustment of Treasury prces to nformaton releases conforms to smlar fndngs by Flemng and Remolona (1999a) and Huang et al (2001) VAR analyss Graphs a-d llustrate estmatons of the cumulatve effects of returns and sgned trades on one another, and of returns on subsequent returns, when the VAR n model (1) s appled to prces and trades recorded for the 2-year note on February 3, Because there are fewer data ponts, fve lags are used n each equaton nstead of ten. As before, the mpulse-response graphs assume that causaton runs from trades to 8 Green (forthcomng), however, fnds that the adverse-selecton component of effectve Treasury bdask spreads rses after nformaton announcements. He nterprets ths result as showng an ncrease n the nformatonal role of tradng. 21

22 returns. Sums of coeffcents for the dfferent tme perods for the two, fve and ten year notes are provded n Table 6. In what follows we wll focus on the results for the two-year note. Cross effects between trades and returns seem to have been stronger on February 3 than they were durng the full two-year sample perod. The mpact of trades on returns s about twce as strong on February 3 as durng the full sample, wth a new buy order leadng, on average, to an ncrease of 0.53 hundredths of a percentage pont n the return (Graph b). The effect of returns on trades s also substantally hgher than normal on February 3: a one standard devaton postve return now leads to a 5.2% ncrease n the lkelhood of a purchase after ten perods, more than 50% hgher than the effect estmated for the sample as a whole (Graph c). The persstence of shocks to returns s also stronger. Ten perods after a postve shock to the return, 77% of the ncrease remans n the bond prce, compared wth 69% for the sample as a whole (Graph a). The autocorrelaton of tradng behavour s weaker, however. A new buy order s followed by an addtonal 0.56 of a net buy over the subsequent ten perods, n contrast to the effect n the broad sample, whch was estmated to be 0.72 (Graph d). These patterns shfted n the course of the day, n ways analogous to the shfts across the dfferent subsamples studed n model (2). Durng the most turbulent perod, 11 am-2 pm, when duraton was at ts shortest, trades had a relatvely stronger effect on returns and were relatvely more autocorrelated than was the case ether before 7 am or after 2 pm. In the 7-11 am and 11 am-2 pm perods, returns had strong postve effects on the drecton of trades, whle after 2 pm ths relatonshp became negatve. The persstence of shocks to returns was much hgher between 11 am and 2 pm, whle before and after ths tme t was about the same as that estmated for the full sample. 3.4 Tradng n volatle condtons: A summary Combnng the evdence from the duraton-based subsamples and from February 3, 2000, t appears that the nteractons between prce movements and trade behavour change n at least two ways at tmes when tradng s volatle and uncertanty s hgh. Frst, the mpact of trades on prce movements (the conventonal adverse selecton effect) s stronger. Second, however, effects n the other drecton - from prce movements to trades - become stronger as well. It s also clear that markets can 22

23 sometmes shft suddenly from one regme to another n terms of the absolute and relatve strengths of these dfferent effects. In the case of February , for example, t appears that postve feedback effects dmnshed substantally as prce movements stablsed n the afternoon, and nformaton-drven prce dynamcs were replaced wth a greater role for nventory adjustments. 5. Conclusons We have found that the nteractons between trades and quote-changes n the US Treasury securtes market tend to change n mportant ways when tradng condtons are rapd and volatle. We examne tradng n the 2-year, 5-year, and -year on-therun treasury notes over the perod January December The mpact of trades on prces tends to become stronger, confrmng a common theoretcal result n the market mcrostructure lterature. The mpact of prces on trades tends to change as well on more volatle days, generally n a postve drecton. As a consequence of these two effects, prce-changes tend to be more postvely (or less negatvely) autocorrelated on days when condtons are more volatle. Ths pattern s evdent when one compares unusually turbulent days wth normal days or unusually quet days. It also emerges from a close analyss of quotes and trades from February 3, 2000, whch was a partcularly volatle tradng day durng ths perod. The models commonly used n the analyss of market mcrostructure emphasse adverse selecton effects resultng from the presence of nformed and unnformed traders n the market. Ths helps to explan the mpact of trades on prces, but a rcher theoretcal approach s necessary to capture the mpact of prces on trades. Such effects mght come out of a model where traders face uncertanty, not just about the fundamental value of an asset, but also about the precson of the sgnals observed by them and by other traders. In such an envronment, a prce movement n a gven drecton could lead a trader to revalue the asset n the same drecton, at least for a short perod of tme. Ths would lead to postve feedback n tradng behavour and, as a result, n returns over short horzons. 23