Round number effects n WTI Crude Ol Futures Market Vctor (Ro) Cho Abstract Round number effects predct excess buyng ust below a round number ($X.99) and excess sellng ust above a round number ($X.01). Usng 148 mllon trade observatons for West Texas (WTI) crude ol futures market for the perod from January 01, 1996 to October 31, 2015, we fnd excess buyng ust below a round number and excess sellng ust above a round number n both pre- and post-electronc perods, confrmng the exstence of round number effects n WTI crude ol futures market. Further, ths paper provdes evdence that hedgers, who are less nformed traders, nfluence round number effects. Earler research nto round number effects focuses on US stock markets only and does not address what type of traders nfluences round number effects. We also examne 24-hour trade return based on round number effects. Prevous lterature documents evdence that round number effects s a maor determnant of 24-hour postve trade return n US stock markets. By contrast, we fnd round number effects s not a determnant of 24-hour postve trade return n WTI crude ol futures market and the average 24-hour trade return based on round number effects s negatve 0.0014 percent. Addtonally, we document evdence that the mpact of the net poston held by hedgers s greater than that of speculators on market lqudty and volatlty n WTI crude ol futures market. We fnd negatve relaton between excess sellng by hedgers and market lqudty and postve relaton between excess buyng by hedgers and market lqudty. We also fnd postve relaton between excess sellng by hedgers and market volatlty but we fnd no evdence that tradng actvty of speculators affect market volatlty. 1
Contents Round number effects n WTI Crude Ol Futures Market... 1 Abstract... 1 1. Introducton... 3 2. Background, Pror Lterature and Hypotheses Development... 7 2.1. Hypothess 1: Round number effects... 7 2.1.1 Left-dgt effects... 8 2.1.2. Threshold trgger effect... 9 2.1.3 Cluster undercuttng effect... 10 2.2. Hypothess 2: Impacts of Tradng actvty of Speculators and hedgers on round number 11 2.3. Hypothess 3: the determnant of 24-hour trade return... 12 2.4. Impacts of dfferent traders poston on prce volatlty... 13 3. Data... 14 3.1. Roll over... 14 3.2. Pre and Post-electronc perod... 14 3.3. Buy-sell mbalances... 15 3.4. Hedger and speculator postons... 16 3.5. Lqudty and volatlty... 17 4. Methodology... 18 5. Emprcal results... 23 5.1. Summary statstcs durng pre-electronc Perod... 23 5.2. Hypothess 1: exstence of round number effects durng pre-electronc perod... 26 5.3. Summary statstcs durng post-electronc perod... 28 5.4. Hypothess 1: exstence of round number effects durng post-electronc perod... 32 5.5. Condtonal Buy-sell Imbalance Tests... 34 5.6. Hypothess 2: mpacts of hedgng and speculatng on round number effects... 37 5.7. Hypothess 3: the determnants of 24-hour trade return... 41 5.8 Robustness... 43 5.8.1 Lqudty and tradng actvty... 43 5.8.2 Volatlty and tradng actvty... 47 6. Concluson... 51 7. Reference... 53 2
1. Introducton A recent research by Bhattacharya, Holden and Jacobsen (2012) provde evdence that stock market traders use a round number as cogntve reference pont for value. Bhattacharya, Holden and Jacobsen (2012) fnd excess buyng ust below a round number ($X.99) and excess sellng ust above a round number ($X.01) by lqudty demanders n U.S common stock markets and they term t round number effects. Ther fndng s most consstent wth psychologcal prcng effect around a round number as dscussed n research n cogntve psychology and marketng (Rosch, 1975; Thomas and Morwtz, 2005). Bhattacharya, Holden and Jacobsen (2012) dscuss three dfferent knds of round number effects (1) left-dgt effect, (2) threshold trgger effect, and (3) the cluster undercuttng effect to explan the excess buyng ust below a round number ($X.99) and excess sellng ust above a round number ($X.01). Bhattacharya, Holden and Jacobsen (2012) further document that round number effects s a maor determnant of 24-hour postve trade return. A large lterature documents the assocaton between tradng actvty and prce clusterng at a round number (Nederhoffer, 1965; Nederhoffer, 1966; Harrs 1991; Grossman, Mller, Cone, Fschel and Ross, 1997; Ikenberry and Weston 2003; Chung, Van Ness and Van Ness, 2004; Davs, Van Ness and Van Ness, 2014). Most studes document nvestors have a preference for a round number because of ts hgh accessblty as dscussed n cogntve psychology and marketng research (Rosch, 1975;Thomas and Morwtz, 2005). The key dfference between the analyss of prce clusterng and round number effects s that the drecton of trades only matters when analysng round number effects. Whle, n most exstng studes, tradng actvty s measured by volume, we measure tradng actvty by order mbalance. Order mbalance, defned as the proporton of net buyer-ntated 1, s a measure of tradng actvty that s suggested as more nformatve than volume (Chorda, Roll and Subrahmanyam, 2002). Motvated by fndngs of Bhattacharya, Holden and Jacobsen, we extend ths lne of the lterature by explorng the exstence of round number effects n West Texas (WTI) crude 1 The net buyer-ntated s defned as the dfference between buyer-ntated and seller-ntated trades 3
ol futures market. The commodty futures markets are dfferent from stock markets n several ways. One of the maor dfferences s that whle stocks are nvestment assets, commodty futures assets are consumpton assets. Therefore, commodty futures markets are for hedgng and speculatng. U.S commodty futures tradng commsson (CFTC) publsh weekly commtment of traders (COT) report that contans long and short postons held by hedgers and speculators. Ths specal feature helps us to separate speculators from hedgers. Ths enables us to examne whether tradng actvty of hedgers or speculators nfluences round number effects. Snce WTI crude ol futures s one of the largest commodty futures markets, the features of WTI crude ol futures should represent the general features of commodty futures markets. In ths paper, usng 152 mllon trade observatons over the perod from January 01, 1996 to October 31, 2015, we explore the exstence of round number effects n WTI crude ol futures market. We dvde the sample perod nto two sub-sample perods: pre and post-electronc perod to examne whether there s any change n round number effects. Followng Bhattacharya, Holden and Jacobsen (2012), we also compute buysell rato n three dfferent ways: the proporton of the net buyer-ntated trades, the proporton of the net volume of buyer-ntated futures contact and the proporton of the net buyer-ntated dollar volume. For all three regressons, we fnd excess buyng ust below a round number and excess sellng ust above a round number durng both pre and post-electronc perods. Thus, we confrm the exstence of round number effects exst n WTI Crude ol futures market. We also examne whch of three round number effects s more prevalent than the other two. Usng nckel as a benchmark, we conducted four condtonal buy-sell mbalance: ask falls below a round number, ask falls to a round number, bd rses to a round number, bd rses above a round number and ther correspondng ask falls below a nckel, ask falls to a nckel, bd rses to a nckel, bd rses above a nckel. Inconsstent wth Bhattacharya, Holden and Jacobsen (2012) who document that cluster undercuttng effect s the domnant round number effects n US stock markets, we fnd that threshold trgger effect s more prevalent than the other two n WTI crude ol futures market. Havng explored the exstence of round number effects WTI crude ol futures market, we examne whether 4
round number effects s a maor determnant of 24-hour trade return as documented n Bhattacharya, Holden and Jacobsen (2012). However, we further fnd conflctng fndng to that of Bhattacharya, Holden and Jacobsen (2012). We fnd no evdence that round number effects s a determnant of 24-hour postve trade return and the average 24- hour trade return based on round number effects s negatve 0.0014 percent n WTI crude ol futures market. As a robustness check, we nclude two market varables market lqudty and volatlty measured by the relatve bd-ask spread and standard devaton of prce return respectvely. Controllng for market lqudty and volatlty separately, we fnd that round number reman persstent. We make several new contrbutons to the lterature on round number effects. Frst, we are the frst study to provde evdence that round number effects exst n commodty futures markets. Second, we explore the trader type that nfluences round number effects. Prevously, Johnson and Shanthkumar (2007) examne whether unnformed traders nfluence stock-prce clusterng n US stock markets but they fnd no evdence. Usng COT, we are able to separate speculators from hedgers and fnd that hedgers, who are less nformed, nfluences round number effects. To our knowledge, we are the frst study to provde evdence that unnformed traders nfluences round number effects. Addtonally, we examne the nteracton between tradng actvty of hedgers and speculators and market lqudty. We fnd that net poston of hedgers has an asymmetrc effect on market lqudty. We provde evdence that there s negatve relaton between excess sellng and market lqudty (.e. wder bd-ask spread) and postve relaton between excess buyng and market lqudty (.e. narrower bd-ask spread). We also examne the nteracton between tradng actvty of hedgers and speculators and market volatlty. We fnd that net poston of hedgers has an asymmetrc effect on market volatlty. We provde evdence that excess sellng by hedgers affect market volatlty. However, we fnd no evdence that tradng actvty of speculators affect market volatlty. The rest of the paper s organsed as follows. Secton 2 dscusses the lterature revew and hypothess development. Secton 3 explans the data source and the selecton of 5
sample data. Secton 4 presents the methodology. Secton 5 presents emprcal evdence on left-dgt effect n commodty futures market. Secton 6 concludes. 6
2. Background, Pror Lterature and Hypotheses Development 2.1. Hypothess 1: Round number effects Our frst hypothess s that there s excess buyng ust below a round number ($X.99) and excess sellng ust above a round number ($X.01). Round number effects predct excess buyng ust below a round number and excess sellng ust above a round number because stock traders use a round number as cogntve reference pont for value. Thus, the theory tells us stock traders are motvated to buy ust below a round number and motvated to sell ust above a round number. Bhattacharya, Holden and Jacobsen (2012) are the frst to test whether there s excess buyng ust below a round number and excess sellng ust above a round number n US stock markets, whch they term round number effects. Usng 100 mllon stock transactons, Bhattacharya, Holden and Jacobsen (2012) fnd excess buyng ust below a round number and excess sellng ust above a round number by lqudty demanders n US stock markets, provdng evdence of the exstence of round number effects n US stock markets. As dscussed above, excess buyng ust below a round number and excess sellng ust above a round number s an mplcaton of round number effects. Ths gves us our frst hypothess. Hypothess 1 (H1). Buy trades should outnumber sell trades ust below a round number (e.g. $X.99) and sell trades should outnumber buy trades ust above a round number (e.g. $X.01) Bhattacharya, Holden and Jacobsen dscuss three dfferent knds of round number effects hypotheses for buy-sell mbalance pattern below and above a round number (1) the left-dgt effect, (2) threshold trgger effect and (3) the cluster undercuttng effect. 7
2.1.1 Left-dgt effects Frst, one vew that holds excess buyng ust below a round number and excess sellng ust above a round number s left-dgt effect. Left-dgt effect s the observaton that leftmost prce dsproportonately affects our percepton of prce. Ths percepton s more lkely to occur when ntroducng a nne endng n the prce. However, t s the change n the leftmost dgt, rather than one cent drop, that affects the magntude of percepton. For example, the psychologcal dfference between $3.00 and $2.99 s greater than the dfference between $2.70 and $2.69 because consumers pay a lot more attenton to the leftmost dgt than rght-hand dgts. To consder evdence, we consder the marketng lterature. Usng 1,415 advertsed retal prces from newspapers, Schndler and Krby (1997) document evdence that 9-endng prce s the most common practce by retalers. Stvng and Wner (1997) document evdence that consumers do not always process all of the numercal nformaton contaned n the prce. Usng the data for two frequently purchased products, tuna and yogurt, Stvng and Wner (1997) fnd that consumers process prces from left-to-rght, begnnng wth leftmost dgts and frequently gnore rght-hand dgts. Schndler and Wman (1989) document evdence that 9-endng prces are less lkely to be recalled accurately and the prce wll be underestmated when t s recalled. Thomas and Morwtz (2005) fnd that consumers perceve 9-endng prce substantally lower than a 0-endng prce only when the leftmost dgt changes. Drawng on the over-representaton of 9-endng n advertsed retal prces by retalers, Brenner and Brenner (1982) conclude we have only a lmted amount of memory and a lmted capacty for storng drectly accessble nformaton. In other words, people have processng lmtaton and there s a lmt on how much nformaton a human beng can deal wth at once or wthn a lmted perod. Hnrchs, Yurko and Hu (1981) document that left-to-rght readng causes people to make decson smply on the bass of the value of the leftmost dgt the most accessble number and storng only the leftmost dgt of a number s a very smple operaton. In lne wth studes on nne-endng prce, a number of retal prcng studes provde evdence that the use of 9-endng prce ncrease demand n retal sales (Anderson, and Smester, 2003; Schndler and Kbaran,1996). 8
2.1.2. Threshold trgger effect The second round number effect s threshold trgger effect. The threshold trgger effect s defned as when a securty prce reaches or cross a round number, a wave of buyng or sellng s trggered. The key dea s nvestors have a preference for round numbers, where the herarchy of roundness from the most round to the least round s whole dollars, half-dollars, quarters, dmes, nckels, and pennes. For example, f the securty prce falls to (or crosses below) a round number, t wll trgger buy trades whereas f the prce rses to (or crosses above) a round number, t wll trgger sell trades. Research n cogntve psychology documents evdence that people employ heurstc to reduce udgements to smpler one when faced wth the dffcult task of udgng the probablty of event (Tversky and Kahneman, 1973). One heurstc that Rosch (1975) documents s that people use cogntve reference ponts as comparson standards to form udgment aganst other stmul (Rosch 1975). In the context of numbers, Rosch (1975) documents that round numbers are cogntve reference ponts because round numbers have hgh cogntve accessblty as they are easer to recall and work wth than non-round numbers. Schndler and Krby (1997) show that round numbers have hgh cogntve accessblty and the hgh cogntve accessblty of round numbers account for the overrepresentaton of 0- and 5-endng prces ( the mdpont of 10) n retal markets. There s a large fnance lterature on prce clusterng at round numbers n fnancal markets. Prce clusterng s a phenomenon where transactons cluster at round numbers. Consstent wth the threshold trgger effects, a number of studes provde evdence of the prce clusterng at round numbers n US stock markets. Usng 1,854 NYSE and AMEX (pre-decmalzaton) transacton dataset durng the week of September 28, 1987, Harrs (1991) document evdence that whole-dollar prces are more common than half-dollar prces, and half-dollar prces are more common than odd quarters, confrmng that prce clusterng s pervasve n US stock markets. Harrs (1991) fnds that clusterng ncreases wth volatlty. Usng post- decmalzaton trade prce and quote dataset of NYSE and NASDAQ for May 2001, Chung, Van Ness and Van Ness (2004) provde evdence that prce clusterng perssts even after the move to decmalzaton, wth prce clusterng on zero-endng prces ($X.X0). Prce clusterng at round numbers s also reported n nternatonal equty markets (Atken, Brown, 9
Buckland, Izan and Walter, 1996; Grossman, Mller, Cone, Fschel and Ross, 1997; Ca, Ca and Keasey 2007; Guo, 2013). Atken, Brown, Buckland, Izan and Walter (1996) fnd prce clusterng on Australan Stock Exchange and also fnd that prce clusterng ncreases volatlty. Ca, Ca and Keasey (2007) fnd prce clusterng on both stock markets (the SHSE and SZSE) n Chna. Other fnancal markets such as IPO aucton (Kandel, Sarg,and Wohl, 2001), currency (Goodhart and Curco, 1990; Osler (2003)), gold (Aggarwal and Lucey, 2005) also report prce clusterng at round numbers. A recent research by Davs, Van Ness and Van Ness (2014) fnds prce clusterng even n a sample that contans hgh-frequency tradng frm s transactons. Usng the database contans the tradng actvty of 26 hgh-frequency tradng frms n 120 stocks on NASDAQ for the year 2009, Davs, Van Ness and Van Ness (2014) document evdence that prce clusterng ncreases wth volatlty when a non-hgh frequency tradng frms provdes lqudty. However, when a hgh-frequency tradng frm provdes lqudty, the varable s not sgnfcant. 2.1.3 Cluster undercuttng effect The last round number effect s the cluster undercuttng effect. Undercuttng occurs when a new lmt sell (buy) s submtted at a penny lower (hgher) than the exstng ask (bd) at a round number. For example, a market buy hts the new ask prce at $2.99 and thus, buy trades are frequently recorded below round numbers. Conversely, a market sell hts the new bd prce at $3.01 and thus, sell trades are frequently recorded above round numbers. The cluster undercuttng effect predcts excess buyng below round numbers and excess sellng above round numbers. Bhattacharya, Holden and Jacobsen document that the cluster undercuttng s the most pervasve round number effects. 10
2.2. Hypothess 2: Impacts of Tradng actvty of Speculators and hedgers on round number Our second hypothess s that the net poston of the trader type that nfluences round number effects s long poston below a round number and short poston above a round number. Excess buyng below a round number and excess sellng above a round number s drven by behavoural bas and therefore, s not assocated wth nformaton motvated tradng. A number of studes documents that unspecalsed traders have no nformaton analysng sklls and therefore, ther trades are more lkely to be motvated by behavoural bas whereas specalsed traders have better analysng sklls and nformaton and trade on nformaton (Nofsnger and Sas, 1999; Kamesaka, Nofsnger and Kawakta, 2003). Research on futures market shows that speculators are better traned and have better resources than hedgers. (Schwarz, 2012; Dewally, Ederngton and Fernando, 2013; Chen and Chang,2015). Earler research on prce clusterng fnds no evdence of what trader type nfluences prce clusterng at round numbers. In the prevous lterature, Bhattacharya, Holden and Jacobsen (2012) do not dscuss what trader type nfluences round number effects. Johnson and Shanthkumar (2007) examne whether unnformed traders nfluences stock-prce clusterng n US stock markets but they fnd no evdence. Davs, Van Ness, and Van Ness (2014) document evdence that better-nformed hgh-frequency traders exhbt less prce clusterng n ther transactons than non-hgh frequency traders. However, Davs, Van Ness, and Van Ness (2014) only suggest that prce clusterng s a result of human bas and provde no evdence that non-hgh frequency traders nfluences prce clusterng. In ths paper, we want to determne and test what trader type nfluences round number effects n WTI crude ol futures market. Ths gves our second hypothess: Hypothess 2 (H2). The net poston of the trader type that nfluences round number effects s long poston ust below a round number (e.g. $X.99) and short poston ust above a round number (e.g. $X.01) 11
2.3. Hypothess 3: the determnant of 24-hour trade return Bhattacharya, Holden and Jacobsen (2012) document evdence that round number effects s a maor determnant of 24-hour postve trade return and a tradng strategy based on round number effects generate $59.8 mllon per year n US stock markets. However, earler research on behavour-based trade shows that specalsed traders, who are better nformed and have better analysng sklls, trade for nformaton because ther net poston s postvely related to ther trade return whereas unspecalsed traders tradng s motvated by behavoural bas because ther net poston s negatvely related to ther trade return (Nofsnger and Sas, 1999; Kamesaka, Nofsnger and Kawakta, 2003). Usng data durng 1977 to 1996 for US stock markets, Nofsnger and Sas (1999) document tradng that earns hgh returns ndcates that the tradng was motvated by nformaton whereas tradng that results n a low return ndcates a behavoural-based motvaton. Kamesaka, Nofsnger and Kawakta (2003) also document strong evdence that tradng wth hgh returns ndcate that the tradng s motvated by nformaton whereas tradng wth low returns ndcate that the tradng s motvated by behavoural bas usng data durng 1980 to 1997 for Tokyo Stock Exchange. In futures market, speculators are specalsed traders because ther net poston s postvely related to ther trade return whereas hedgers are unspecalsed traders because ther net poston s negatvely related to ther trade return (Schwarz, 2012; Dewally, Ederngton and Fernando, 2013; Chen and Chang,2015). Usng data durng 1993 1997 for energy futures market, Dewally, Ederngton and Fernando (2013) document evdence that mean hedger profts are negatve whereas speculator profts are postve and conclude that traders who hold net postons opposte sgn to hedgers have hgher profts than traders whose net postons algn wth hedgers. We examne whether round number effects s a maor determnant of 24-hour postve trade return as documented n Bhattacharya, Holden and Jacobsen (2012) n WTI crude ol futures market. Ths gves us our thrd hypothess. 12
Hypothess 3 (H4). Round number effects s a maor determnant of 24-hour postve trade return 2.4. Impacts of dfferent traders poston on prce volatlty Addtonally, we examne the mpacts of tradng actvty of hedgers and speculators on market lqudty and volatlty n WTI crude ol futures market. The boom and bust n commodty prces durng 2006 2008 accompaned by substantal ncrease n tradng actvty of speculators and commodty nvestng (.e. fnancalzaton of commodty markets) has led to a renewed nterest n the potental effect of commodty futures tradng. There s ongong debate as to whether the tradng actvty of speculators has a destablzng role by ncreasng volatlty n commodty market. Thus, we partcularly focus on the mpacts of speculaton actvty on WTI crude ol futures market. The evdence s mxed. Sanders, Irwn and Merrn (2010) and Tll (2009) fnd that speculaton rses merely as a response to a rse n hedgng demand and speculaton s not to be blamed for the boom and bust of 2008 n commodty futures prce. Buyuksahn and Harrs (2011) test whether speculators has destablzng effect on commodty futures market and fnd lttle evdence that speculaton has harmful mpact. However, the percepton of the general publc and polcy makers s that there was actually excessve speculaton n the commodty futures markets whch had a destablzng effect on prce durng the boom and bust of 2008. Accordng to Chang, Chen, Chou, and Gau (2013), n 2009, the Commodty Futures Tradng Commsson (CFTC) mposed poston lmts n an attempt to control excessve speculaton and stablze prce movements n some futures markets ncludng Crude ol futures. 13
3. Data We use tck hstory data for West Texas lght (WTI) crude ol futures market for the perod from January 01, 1996 to October 31, 2015 from Thomson Reuters Tck Hstory (TRTH). TRTH database began n 1996, so ths s the startng pont. We collect tck data on quote and trade prce, trade volume, and the bd and ask quotes at a mllsecond frequency. We use one-hundred twenty WTI futures contracts. Our quote and transacton data cover both open-outcry and electronc tradng. 3.1. Roll over In order to avod thn tradng and expraton effects, we follow De Vlle de Goyet, Dhaene, and Sercu (2008) to construct contnung seres of the most actvely traded contracts. Followng De Vlle de Goyet, Dhaene, and Sercu (2008), we replace a contract that expres n month m wth the next nearest-to-maturty contract on the last day of month m 1. For example, March contract (CLH) expres n February (month m) but ts most actvely traded perod s January (month m 1). Thus, we only consder quotes and trades from January (month m 1) for the March contract. Specfcally, on the last day of month m 1, the last trade prce s the last observaton of the exprng contract whereas on the frst day of month m, the frst trade prce s the frst observaton of the new contract. Ths ensures that at roll-over. In total, we have over one-hundred ffty-two mllon trade observatons across one-hundred twenty actve WTI crude ol futures contracts. 3.2. Pre and Post-electronc perod Pror to September 3rd, 2006, tradng on U.S futures market was entrely n the openoutcry market. Now, tradng s largely on the electronc platform and ntermedated largely by electronc market makers. We dvde our sample data nto two subsample perods pre and post-electronc perods to explore the exstence of round number effects and to examne whether there was any change n round number effects. 14
The data sample for the pre-electronc perod s based on all trades and quotes over the perod from January 1, 1996 to September 2nd, 2006, contanng a total of over 3.9 mllon trade observatons. We begn our post-electronc sample perod on September 3rd, 2006. The post-electronc sample perod s based on all trades and quotes over the perod from September 3rd, 2006 to October 31, 2015, contanng a total of over 148 mllon trade observatons. 3.3. Buy-sell mbalances We follow the algorthm presented n Lee and Ready (1991) to assgn a trade drecton to each trade. We assgn a buy f the transacton prce s above the bd-ask mdpont and a sell f the transacton prce s below the bd-ask mdpont. The mdpont s defned as the average of the best bd and best ask prces. Trades executed exactly at the mdpont are classfed as nether buyer nor seller ntated and consdered as no trade. For each.xx prce pont, we aggregate all buys and all sells (for example, at $39.99, $40.99, $41.99, etc are aggregated at the.99 prce pont) for each day (or each week) and compute the buy-sell rato. For each day (or each week) nterval, we defne the buysell rato as Buy sell Rato t, = Buy t, Sell t, Buy t, + Sell t, (1) where Buy t, s the number of buys at.xx prce pont on day t and Sell,t s the number of sells at.xx prce pont on day t. Bhattacharya, Holden and Jacobsen (2012) compute the buy-sell rato n three dfferent ways as the number of buyer- less the number of seller-ntated trades, the number of buyer-ntated shares purchased less the number of seller-ntated shares sold and the dollars pad by buyer-ntators less the dollars receved by seller ntators. For all three buy-sell rato measures, Bhattacharya, Holden and Jacobsen (2012) fnd excess buyng ust below a round number and excess sellng ust above a round number. 15
We also compute buy-sell rato n three dfferent ways. For each day (or each week) nterval we compute the followng: OIB# t, : the proporton of the net buyer-ntated trades at.xx prce pont on day t; 2 OIBvol t, : the proporton of the net volume of buyer-ntated futures contact at.xx prce pont on day t; 3 OIB$ t, : the proporton of the net buyer-ntated dollar volume at.xx prce pont on day t; 4 3.4. Hedger and speculator postons U.S Commodty Futures Tradng Commsson (CFTC) collects data on traders postons n futures market. CFTC collect the poston of commercal (commonly referred to as hedgers) and non-commercal traders (commonly referred to as speculators) and aggregates these data nto commtment of traders (COT) report every Tuesday and publsh t n the followng Frday. Thus, the COT reflects postons as of the precedng Tuesdays. The COT report categorses postons nto hedgers and speculators. Hedgers has some physcal dealngs or commercal nteracton wth the underlyng commodty and therefore face prce rsks n the cash market that they seek to offset or hedge n futures market. Speculators hold postons opposte those of hedgers, thereby provdng lqudty to the market wthout necessarly sufferng any physcal rsk exposure that needs to be offset. The nformaton n the COT reports allows us to separate speculators from hedgers. Ths enables us to examne whether tradng actvty of hedgng or speculatng nfluences round number effects. We use the weekly COT for the post-electronc perod from September 7, 2006 to 31 October 2015. 2 The net buyer-ntated s defned as number of buyer-ntated trades less the number of seller-ntated trades 3 The net volume of buyer-ntated futures contact s defned as the volume of buyer-ntated futures contact less the volume of seller-ntated futures 4 The net buyer-ntated dollar volume s defned as the buyer-ntated dollar volume less seller-ntated dollar volume 16
For each week nterval, we compute the net poston to proxy for the tradng actvty of hedgers and speculators. The net poston of for each category of traders s defned as T t, = Long t, Short t, Long t, + Short t, (2) where Long,t and Short,t s long and short poston of trader type at.xx prce ponts n week t and T t, s the net poston of trader type at.xx prce ponts n week t and defned as the proporton of net long poston (.e. net buy-ntated trades) at prce ponts n week t To examne the relaton between net postons (.e. order flow) of dfferent traders and buy-sell ratos, we aggregate all buys and all sells for each week nstead of each day for each.xx prce pont and compute buy-sell rato. 3.5. Lqudty and volatlty For each week nterval, we compute the followng measures of lqudty and volatlty: We use s the relatve bd-ask spread to proxy for the lqudty. We calculate the relatve bd-ask spread by takng the dfference between bd prce and ask prce and then dvde t by the average of the bd and ask prce (.e. mdpont prce). For each.xx prce pont, we take the average bd-ask spread for each week durng the post-electronc perod. Spread t, : the relatve bd-ask spread at.xx prce ponts n week t We use the standard devaton of prce return to proxy for the volatlty. We measure prces n natural logs and calculate returns usng the percentage change n the last traded prce. For each.xx prce pont, we calculate the standard devaton of prce return for each week durng the post-electronc perod. retvol t, : the volatlty at.xx prce ponts n week t 17
4. Methodology Our frst hypothess s to test whether round number effects exst n WTI Crude ol futures market. Excess buyng ust below a round number ($X.99) and excess sellng ust above a round number ($X.01) s the mplcaton of round number effects. We formally test the exstence of round number effects n WIT Crude ol market for both pre and post-electronc perods by runnng the regresson of buy-sell rato on prce ponts, wth partcular focus on ust below a round number and ust above a round number. We mplement three-regressons based on three versons of the buy-sell ratos: OIB#, OIBvol and OIB$. A postve coeffcent on ust below a round number ndcates excess buyng and a negatve coeffcent on ust above a round number ndcates excess sellng. The followng model tests the frst hypothess: Buysell t, = α t, + β 1 X t,01 + β 2 X t,49 + β 3 X t,51 + β 4 X t,99 + ε t, (3) where the dependent varable Buysell t, s the buy-sell rato at.xx prce ponts on day t and X t,01, X t,49, X t,51, X t,99 are prce ponts dummy varables for $X.01, $X.49, $X.51 and $X.99 on day t. In condtonal buy-sell mbalance test, we explore whch of three round number effects domnate n WTI crude ol futures market. Followng, Bhattacharya, Holden and Jacobsen (2012), we test whether buy trades outnumber sell trades after ask prces fall ust below a round number and sells outnumber ther buys after bd prces rse ust above a round number. We use nckel as a benchmark to round number. We conduct four condtonal buy-sell mbalance: ask falls below round number, ask falls to round number, bd rses to round number, bd rses above round number samples and ther correspondng ask falls below nckel, ask falls to nckel, bd rses to nckel, bd rses above nckel samples. We use t-statstc to assess the sgnfcance. t-statstc s computed as follow tstat = x 1 x 2 σ 1 n 1 + σ 2 n 2 18
(4) where x 1s ether medan or mean buy-sell ratos, σ 1 s the standard devaton, and n 1 s the number of observaton for round numbers and x 2s ether medan or mean buy-sell ratos, σ 2 s the standard devaton, and n 2 s the number of observaton for nck benchmarks Our second hypothess s to explore what type of traders nfluences round number effects. Usng COT data, we want to determne what knd of traders (.e. hedgers or speculators) nfluences round number effects n futures market. We use the net poston defned n equaton (2) to proxy for the tradng actvty of dfferent types of traders. We expand the regresson model n equaton (3) to nclude nteracton varables that captures the tradng actvty of hedgers and speculators at prce ponts $X.01, $X.49, $X.51 and $X.99 to test for the second hypothess. Snce COT provdes weekly data, for each.xx prce pont, we aggregate all buys and all sells (for example, at $39.99, $40.99, $41.99, etc are aggregated at the.99 prce pont) for each week and compute the buy-sell rato. We then mplement three-regressons based on three versons of the buy-sell ratos as n the followng model: Buysell t, = α + β 1 X t,01 + β 2 X t,49 + β 3 X t,51 + β 4 X t,99 + α 1 X t,01 T t,01 + α 3 X t,51 T t,51 + α 4 X t,99 T t,99 + β 5 T t, + ε + α 2 X t,49 T t,49 where the dependent varable Buysell t s the buy-sell rato at.xx prce ponts n week t and X t,01, X t,49, X t,51, X t,99 are prce ponts dummy varables for $X.01, $X.49, $X.51 and $X.99 n week t. T t, s the net poston of trader type at.xx prce ponts n week t and X t,01 T t,01, X t,49 T t,49, X t,51 T t,51, X t,99 T t,99 are the net poston held by trader type at prce ponts $X.01, $X.49, $X.51 and $X.99 n week t. (5) The net poston of the trader type that nfluences round number effects ust below a round number s long poston and ust above a round number s short poston. A postve coeffcent on nteracton term for ust below a round number ndcates long 19
poston and a negatve coeffcent on nteracton term for ust above a round number ndcates short poston. Our thrd hypothess tests whether round number effects s a maor determnant of 24- hour postve trade return n WTI crude ol futures market as documented n Bhattacharya, Holden and Jacobsen (2012). If traders use a round number as reference pont for value, a potental proftable strategy s sell above a round number and buy below a round number. We compute 24-hour trade return as follow. For every buy trade observaton ust below a round number (X.99), we buy at the actual trade prce below a round number and sell at the bd prce 24 hours later to close the poston and compute 24-hour trade return. For example, f there s a buy at 11:00 a.m. on day t, we sell at the bd prce at 11:00 a.m. on the next day t + 1. Smlarly, for every sell trade observaton above a round number (X.X01), we sell at the actual trade prce above a round number and buy at the ask prce 24 hours later to close the poston and compute 24-hour trade return. For each.xx prce pont, we end up wth two return categores: (1) the 24-hour trade return to buy, (2) the 24-hour trade return to sell. We take the medan 24-hour trade return by takng the dfference between medan 24-hour trade return to buy and medan 24-hour trade return to sell. We then run the regresson of 24-hour trade return on prce ponts as n the followng model: 24hour trade return t, = α,t + β 1 X t,01 + β 2 X t,49 + β 3 X t,51 + β 4 X t,99 + ε,t (6) where the dependent varable s 24-hour trade return at.xx prce ponts on day t and X t,01, X t,49, X t,51, X t,99 are prce ponts dummy varables for $X.01, $X.49, $X.51 and $X.99 on day t A postve coeffcent on ntercept ndcates that average 24-hour trade return s postve. Next, as a robustness check, we control for lqudty and volatlty. Frst, we test whether round number effects persst after controllng for the lqudty. We use s the relatve bd-ask spread to proxy for lqudty. We calculate the relatve bd-ask spread by takng 20
the dfference between bd prce and ask prce and then dvde t by the average of the bd and ask prce (.e. mdpont prce). For each.xx prce pont, we take the average bd-ask spread for each week durng the post-electronc perod. A hgh bd-ask spread ndcates low lqudty. A postve coeffcent mples wder bd-ask spread (.e. larger tradng costs) and lower market lqudty condtons whereas a negatve coeffcent mples narrower bd-ask spread (.e. smaller tradng costs) and hgher market lqudty condtons n commodty futures market. We also nclude nteracton varables that captures mpacts of net postons held by dfferent trader types at prce ponts $X.01, $X.49, $X.51 and $X.99 on lqudty. We estmate the followng regresson to test whether round number effects persst after controllng for lqudty: Buysell t, = α t, + β 1 X t,01 + β 2 X t,49 + β 3 X t,51 + β 4 X t,99 + α 1 X t,01 T t,01 + α 3 X t,51 T t,51 + α 6 X t,49 T t,49 + β 6 Spread t, + ε t, + α 4 X t,99 T t,99 + β 5 T t, + α 5 X t,01 T t,01 Spread t,01 + α 2 X t,49 T t,49 Spread t,49 + α 7 X t,51 T t,51 Spread t,51 + α 8 X t,99 T t,99 Spread t,99 where the dependent varable Buysell t, s the buy-sell rato at.xx prce ponts n week t and X t,01, X t,49, X t,51, X t,99 are prce ponts dummy varables for $X.01, $X.49, $X.51 and $X.99 n week t, T t, t and X t,01 T t,01 s the net poston of trader type at.xx prce ponts n week, X t,49 T t,49, X t,51 T t,51, X t,99 T t,99 are the net poston held by trader type at prce ponts $X.01, $X.49, $X.51 and $X.99 n week t. Spread t, s the relatve bd-ask spread at.xx prce ponts n week t and X t,01 T t,01 Spread t,01, X t,49 T t,49 Spread t,49, X t,51 T t,51 Spread t,51, X t,99 T t,99 Spread t,99 are nteracton varables that capture the mpact of the net poston held by trader type on lqudty at prce ponts $X.01, $X.49, $X.51 and $X.99 n week t. (7) Next, we test whether round number effects persst after controllng for volatlty. We use the standard devaton of prce return to proxy for the volatlty. We measure prces n natural logs and calculate returns usng the percentage change n the last traded prce. 21
For each.xx prce pont, we calculate the standard devaton of prce return for each week durng the post-electronc perod. We nclude nteracton varables that captures mpacts of net postons held by dfferent trader types at prce ponts $X.01, $X.49, $X.51 and $X.99 on volatlty. Addtonally, we also examne mpacts of net postons of hedgers and speculators on volatlty. We estmate the followng regresson to test whether round number effects persst after controllng for volatlty: Buysell t, = α t, + β 1 X t,01 + β 2 X t,49 + β 3 X t,51 + β 4 X t,99 + α 1 X t,01 T t,01 + α 3 X t,51 T t,51 + α 6 X t,49 T t,49 + β 6 retvol t, + ε t, + α 4 X t,99 T t,99 + β 5 T t, + α 5 X t,01 T t,01 retvol t,01 + α 2 X t,49 T t,49 retvol t,49 + α 7 X t,51 T t,51 retvol t,51 + α 8 X t,99 T t,99 retvol t,99 where the dependent varable Buysell t s the buy-sell rato at.xx prce ponts n week t and X t,01, X t,49, X t,51, X t,99 are prce ponts dummy varables for $X.01, $X.49, $X.51 and $X.99 n week t. T t, s the net poston of trader type at.xx prce ponts n week t and X t,01 T t,01, X t,49 T t,49, X t,51 T t,51, X t,99 T t,99 are the net poston held by trader type at prce ponts $X.01, $X.49, $X.51 and $X.99 n week t. retvol t, s volatlty at.xx prce ponts n week t and X t,01 T t,01 X t,99 T t,99 retvol t,01, X t,49 T t,49 retvol t,49, X t,51 T t,51 retvol t,51, retvol t,99 are nteracton varables that capture the mpact of the net poston held by trader type on volatlty at prce ponts $X.01, $X.49, $X.51 and $X.99 n week t (8) 22
Medan buy-sell rato 5. Emprcal results 5.1. Summary statstcs durng pre-electronc Perod To obtan a prelmnary vew of the exstence of round number effects, we present descrptve statstcs for the medan buy-sell rato for each day at prce ponts from X.01 to X.99 durng the pre-electronc perod (January 1, 1996 to September 2nd, 2006) n Fgures 1-4. The buy-sell rato patterns at prce ponts n Fgures 1-3 resembles that of documented n Bhattacharya, Holden and Jacobsen (2012). The sample ncludes total of over 3.9 mllon trade observatons. Fgure 1 shows the medan proporton of the net buyer-ntated trades by.xx prce pont, Fgure 2 shows the medan proporton of the net volume of buyer-ntated futures contact by.xx prce pont and Fgure 3 shows the medan proporton of the net buyer-ntated dollar volume by.xx prce pont. These medan buy-sell rato fgures show a regular pattern every ten cents. All three fgures show that at trade prce endng n X.X9 buy trades exceeds sell trades whereas at trade prce endng n X.X1 sell trades exceeds buy trades. The man message emergng from Fgures 1 4 s that round number effects exst n WTI crude ol futures market. Fgures 1 3 are the evdence n favour of Threshold trgger effect as X.X0 and X.X5 are round numbers n decreasng order of roundness. As the left-dgt changes around X.X0, Fgures 1 3 are also evdence n favour of left-dgt effect. Fgure 1 Medan proporton of the net buyer-ntated trades at.xx Prce Ponts 0.25 0.99 0.2 0.19 0.29 0.39 0.89 0.15 0.09 0.24 0.34 0.44 0.49 0.69 0.79 0.94 0.74 0.84 0.1 0.04 0.14 0.54 0.59 0.64 0.05 0-0.05 0.26 0.41 0.46 0.31 0.36 0.86-0.1 0.06 0.16 0.91 0.01 0.21 0.51 0.76 0.81 0.96-0.15 0.11 0.61 0.66 0.71-0.2 Fgure 1 Medan proporton of the net buyer-ntated trades at.xx Prce Ponts 23
Medan dollar Bought-Sold Rato Medan volume bought-sold rato Fgure 2 Medan proporton of the net volume of buyer-ntated futures contact at.xx Prce Ponts 0.3 0.19 0.2 0.04 0.09 0.14 0.24 0.29 0.39 0.44 0.49 0.59 0.69 0.74 0.79 0.89 0.94 0.84 0.99 0.1 0.34 0.54 0.64 0-0.1-0.2-0.3 0.06 0.11 0.01 0.16 0.26 0.21 0.36 0.31 0.41 0.46 0.66 0.61 0.56 0.51 0.71 0.76 0.81 0.91 0.86 0.96-0.4 Fgure 2 Medan proporton of the net volume of buyer-ntated futures contact at.xx Prce Ponts 0.3 0.2 0.1 0 Fgure 3 Medan proporton of the net buyer-ntated dollar volume at.xx Prce Ponts 0.19 0.29 0.44 0.09 0.49 0.59 0.69 0.79 0.14 0.89 0.92 0.99 0.04 0.24 0.39 0.74 0.84 0.34 0.64 0.54-0.1-0.2-0.3 0.06 0.11 0.01 0.26 0.16 0.21 0.31 0.36 0.41 0.46 0.56 0.51 0.61 0.66 0.71 0.91 0.86 0.76 0.81 0.96-0.4 Fgure 3 Medan proporton of the net buyer-ntated dollar volume at.xx Prce Ponts 24
Buy-Sell rato 20.00% Buy-Sell Rato by Penny-Endng Prce Pont 15.00% 10.00% 5.00% 0.00% -5.00% -10.00% -15.00% -20.00% 0 1 2 3 4 5 6 7 8 9 Buy-Sell rato by each endng dgt Volume bought-sold rato by each endng dgt Dollar bought-sold rato by each endng dgt Fgure 4 Buy-sell Rato by Penny-Endng Prce Ponts Fgure 4 explores ths further by showng the medan buy-sell ratos by penny-endng prce ponts: X0,.X1,,.X9. Interestngly, the pattern of buy-sell ratos by pennyendng prce ponts s nearly dentcal for all three buy-sell rato measures and all three buy-sell ratos show that the hghest ratos of buy-sell occurs trade prces endng n.x9, and the lowest rato of buy-sell occurs at trades endng n.x1. Smlarly, the second hghest ratos of buy-sell occurs trade prces endng n.x4, and the second lowest rato of buy-sell occurs at trades endng n.x6. In other words, the largest mbalances occur at the prce ponts surroundng X.X0 and the next largest mbalances occur at the prce ponts surroundng X.X5. Fgure 4 s the evdence n favour of Threshold trgger effect as dollars and half-dollars n decreasng order of roundness. As the left-dgt changes around X.00 and X.X0, Fgure 4 s also n favour of left-dgt effect. Fnally, Fgures 1 4 are also evdence n favour of the clusterng undercuttng effect as ths effect occurs around X.00 and X.X0. Lmt orders clustered on X.X0 are undercut by lmt sells at.x9 to yeld excess buyng at.x9, and undercut by lmt buys at.x1 to yeld excess sellng at.x1. Fgures 1 4 suggest that buyng and sellng at each prce pont s not unformly dstrbuted and the buy-sell mbalance patterns at each prce pont share the same lmtaton: they are based on statc prces. 25
The above observatons lead us to examne the exstence of round number effects n commodty futures market. We formalze these observatons n the next secton by estmatng the regresson as specfed n equaton (5). 5.2. Hypothess 1: exstence of round number effects durng pre-electronc perod In ths secton, we examne evdence of exstence of round number effects durng the pre-electronc perod. Here, the obectve s to explore whether round number effects exst n WTI crude ol futures market. In Table 1, we present test results of hypothess 1 as specfed n equaton (4) for three regressons based on three versons of buy-sell ratos. Results n Table 1 show that for all three regressons, the coeffcents on ust below a round number (X.99) are all postve and statstcally sgnfcant at 1 percent level, ndcatng excess buyng ust below a round number. The results support the marketng research by Thomas and Morwtz (2005) who fnd 9-endng prce s perceved to be substantally lower than a 0-endng prce when the leftmost dgt changes. The results show that the opposte s true for the coeffcents ust above a round number (X.01). The coeffcents on ust above a round number are all negatve and statstcally sgnfcant at 1 percent level, ndcatng excess sellng ust above a round number. These results are consstent wth the predcton of round number effects and we confrm the exstence of round number effects n WTI crude ol futures market. The fndng of excess buyng ust below a round number (X.99) and excess sellng ust above a round number (X.01) s consstent wth prevous research (Bhattacharya, Holden and Jacobsen, 2012). In addton, the results n Table 1 also show that for all three regressons, the coeffcents on ust below a half-dollar are all postve and statstcally sgnfcant at 1 percent level and the coeffcents on ust above a half-dollar are all negatve and statstcally sgnfcant at 1 percent level. The results are consstent wth threshold trgger effect that nvestors have a preference for round numbers where the herarchy of roundness from the most round to the least round s whole dollars, half-dollars (.e. the mdpont of round number), quarters, dmes, nckels and pennes. 26
Overall, we fnd evdence that round number effects exst durng the pre-electronc perod. Table 1 Three regressons based on three versons of buy-sell ratos on prce ponts $X.01, $X.49, $X.51 and $X.99 OIB# p-value OIBVol p-value OIB$ p-value Intercept 0.0141 0.0000 *** 0.0063 0.1409 *** 0.0070 0.1029 *** X t,01-0.1142 0.0001 *** -0.1624 0.0001 *** -0.1619 0.0001 *** X t,49 0.1158 0.0001 *** 0.1518 0.0003 *** 0.1524 0.0003 *** X t,51-0.1248 0.0000 *** -0.2290 0.0000 *** -0.2294 0.0000 *** X t,99 0.1552 0.0000 *** 0.1572 0.0002 *** 0.1589 0.0002 *** ***,**,* Means statstcally sgnfcant at the 1 %, 5%, and 10% level respectvely Buysell t, = α t, + β 1 X t,01 + β 2 X t,49 + β 3 X t,51 + β 4 X t,99 + ε t, where the dependent varable Buysell t, s the buy-sell rato at.xx prce ponts on day t and X t,01, X t,49, X t,51, X t,99 are prce ponts dummy varables for $X.01, $X.49, $X.51 and $X.99 on day t. The data sample for the pre-electronc perod s based on all trades and quotes over the perod from January 1, 1996 to September 2nd, 2006, contanng a total of over 3.9 mllon trade observatons. (4) 27
Sep-06 Feb-07 Jul-07 Dec-07 May-08 Oct-08 Mar-09 Aug-09 Jan-10 Jun-10 Nov-10 Apr-11 Sep-11 Feb-12 Jul-12 Dec-12 May-13 Oct-13 Mar-14 Aug-14 Jan-15 Jun-15 5.3. Summary statstcs durng post-electronc perod We contnue explorng the exstence of round number effects for the post-electronc perod. On September 3, 2006, U.S. commodty futures market ntroduced the electronc platform and snce then there has been a substantal ncrease n tradng actvty of speculators and commodty nvestng n commodty futures market as shown n Fgure 5 and 6. In our data, whle we only observe the total of 3.9 mllon trade observatons durng the pre-electronc perod, we observe the total of 148 mllon trade observatons n the post-electronc perod and that s nearly 38 tmes more trade observatons than that of post-electronc perod. Durng the boom and bust of commodty prce n 2008, nvestors held ther bggest poston on record n the commodty futures market. 350000 Tradng Volume Actvty 300000 250000 200000 150000 100000 50000 0 Fgure 5 shows the Crude ol futures daly average tradng volume (n contracts) from September 03, 2006 to October 31, 2015 28
Sep-06 Feb-07 Jul-07 Dec-07 May-08 Oct-08 Mar-09 Aug-09 Jan-10 Jun-10 Nov-10 Apr-11 Sep-11 Feb-12 Jul-12 Dec-12 May-13 Oct-13 Mar-14 Aug-14 Jan-15 Jun-15 18000000 16000000 14000000 12000000 10000000 8000000 6000000 4000000 2000000 0 Dollar Fgure 6 shows the WTI daly average dollar tradng from September 2006 to October 2015 To obtan a prelmnary vew of the exstence of round number effects n the postelectronc perod (September 3rd, 2006 to October 31, 2015), we present descrptve statstcs for medan buy-sell rato for each day at prce ponts from X.01 to X.99 durng the post-electronc perod n Fgures 7-10. Fgure 7 shows the medan proporton of the net buyer-ntated trades by.xx prce pont, Fgure 8 shows the medan proporton of the net volume of buyer-ntated futures contact by.xx prce pont and Fgure 9 shows the medan proporton of the net buyer-ntated dollar volume by.xx prce pont. Fgures 7 9 show smlar buy-sell rato patterns to that of pre-electronc perod. All three fgures show that at trade prce endng ust below dollars, half-dollars, quarters, dmes and nckels (.e. X.99, X.49, X.24, X.09, X.04) buy trades exceeds sell trades whereas at trade prce endng ust above dollars, half-dollars, quarters, dmes and nckels (.e. X.01, X.51, X.26, X.11, X.06) sell trades exceeds buy trades. Fgures 7 9 are the evdence n favour of Threshold trgger effect as dollars, half-dollars, quarters, dmes and nckels are round numbers n decreasng order of roundness. As the left-dgt changes around X.X0, Fgures 7 9 are also evdence n favour of left-dgt effect. 29