Option Trading Costs Are Lower Than You Think

Transcription

1 Opion Trading Coss Are Lower Than You Think Dmiriy Muravyev Boson College Neil D. Pearson Universiy of Illinois a Urbana-Champaign March 15, 2015 Absrac Convenionally measured bid-ask spreads of liquid equiy opions are large. This presens a puzzle, which we resolve. A high frequency, changes in opion prices can be prediced using recen changes in sock prices. A large proporion of opion rades exploi his predicabiliy o ake liquidiy a low cos, buying and selling immediaely before opion prices are expeced o change. Convenional measures of effecive spreads and price impac do no accoun for his execuion iming bu can be adjused o do so. For he average rade, effecive spreads ha ake accoun of rade iming abiliy are one-hird smaller han he convenionally measured effecive spreads; for rades ha reflec execuion iming, hey are five imes smaller. These findings have sriking implicaions for he profiabiliy of opions rading sraegies ha involve aking liquidiy. In addiion, convenional measures of price impac oversae i by a facor of more han wo. Our resuls also indicae ha mos opion rades originae from invesors who ime execuions, for example proprieary raders and insiuional invesors who have access o execuion algorihms. Keywords: Execuion iming, rading coss, effecive spread, liquidiy, equiy opions, algorihmic rading We graefully hank Nanex and Eric Hunsader for providing he rade and quoe daa for he opions and heir underlying socks. Mos of he resuls in his paper were included in a previous working paper ha circulaed under he ile Negaive Exernaliy of Algorihmic Trading: Evidence from he Opion Marke. We hank Nicholas Hershey, Richard Payne, Chrisina Scherrer, and seminar or conference paricipans a Boson College, he Commodiy Fuures Trading Commission, he Universiy of Illinois a Urbana- Champaign, he Universiy of Souhern California, Invesmen Technology Group, he Universiy of Connecicu, he Workshop on High-frequency and Algorihmic Trading a he Ciy Universiy of Hong Kong, he Fifh Risk Managemen Conference a Mon Tremblan, and he European Winer Finance Conference for heir commens and suggesions. addresses: muravyev@bc.edu (D. Muravyev), pearson2@illinois.edu (N. D. Pearson)

2 Opion Trading Coss Are Lower Than You Think March 15, 2015 Absrac Convenionally measured bid-ask spreads of liquid equiy opions are large. This presens a puzzle, which we resolve. A high frequency, changes in opion prices can be prediced using recen changes in sock prices. A large proporion of opion rades exploi his predicabiliy o ake liquidiy a low cos, buying and selling immediaely before opion prices are expeced o change. Convenional measures of effecive spreads and price impac do no accoun for his execuion iming bu can be adjused o do so. For he average rade, effecive spreads ha ake accoun of rade iming abiliy are one-hird smaller han he convenionally measured effecive spreads; for rades ha reflec execuion iming, hey are five imes smaller. These findings have sriking implicaions for he profiabiliy of opions rading sraegies ha involve aking liquidiy. In addiion, convenional measures of price impac oversae i by a facor of more han wo. Our resuls also indicae ha mos opion rades originae from invesors who ime execuions, for example proprieary raders and insiuional invesors who have access o execuion algorihms. Keywords: Execuion iming, rading coss, effecive spread, liquidiy, equiy opions, algorihmic rading

3 1. Inroducion A firs glance, opion marke bid-ask spreads are puzzling. In our daa on some of he mos liquid and acively raded opions, quoed opion bid-ask spreads average 8.1 cens per share. Spreads are even wider for opions ha are well in-he-money. Convenionally measured effecive spreads, which reflec he fac ha rades end o occur when quoed spreads are narrow, average 6.2 cens per share. For comparison, he average opion price in our sample is $1.70. To he exen ha hese quoed and effecive spreads measure he coss of aking liquidiy in he opions marke, he coss of aking liquidiy are high. In conras, he spreads on he opions underlying socks average 1.4 cens per share, and ofen are only one cen per share. Puzzlingly, quoed opion bid-ask spreads did no change much during our sample period of April 2003 o Ocober 2006 despie he more han doubling of opion rading volume from 2003 o 2006, by which ime opion rading volume was 17% of sock rading volume. 1 The failure of quoed spreads o decline appears o be inconsisen wih boh heories in which reducions in rading coss increase rading volume and heories in which increases in rading volume lead o lower coss per uni. Our sample period is also he period during which algorihmic rading came o dominae he opion markes, making he failure of quoed spreads o decline even more surprising. Who is paying hese high quoed spreads? Exising heories are also unable o explain why spreads of opions on he same underlying sock increase wih opion moneyness and he high spreads of in-he-money opions. This paern canno be explained by hedge rebalancing coss incurred by opion marke makers, because hedges of well in-he-money opions rarely need o be rebalanced. Similarly, he paern canno be explained by marke makers coss of hedging gamma and vega risks, because well in-he-money opions are no exposed o hese risks. Moreover, hrough he pu-call pariy relaion in-he-money calls (pus) have gamma and vega risks similar o hose of heir corresponding ou-of-he-money pus 1 Daa from he Opions Clearing Corporaion indicaes ha equiy (no including index) opions on approximaely 83 and 184 billion shares raded during 2003 and 2006, respecively (hp:// During 2013 opion rading volume was 27% of sock rading volume compued using CRSP daa, which includes rading in non-opionable socks 1

4 (calls), bu much differen spreads. The large differences beween he spreads of opions and heir underlying socks also canno be explained by differences in he adverse selecion componen of he spread, unless informed raders are much more common in he opions marke han in he sock marke and hey choose o rade in-he-money opions raher han a- or ou-of-he-money opions wih more embedded leverage. The low bid-ask spreads in he sock marke imply ha opion spreads also are oo large o be explained by opion marke makers coss of execuing he iniial dela hedge rades. The exising lieraure has aemped o explain opion quoed and effecive spreads using proxies for iniial dela hedging coss, hedge rebalancing coss, and asymmeric informaion, and achieved limied success (Jameson and Wilhelm 1992, George and Longsaff 1993, Cho and Engle 1999, De Fonnouvelle e al 2003, Kaul e al 2004, Engle and Neri 2010, and Goyenko e al 2014). Mos of hese papers sudy eiher S&P 100 opions or small numbers of equiy opions using shor daa samples, and mos do no use daa from he curren marke environmen following he Opions Linkage and he widespread adopion of algorihmic rading. 2 This lieraure uses regression analyses o produce evidence ha proxies for he iniial dela hedging coss, hedge rebalancing coss, and asymmeric informaion are correlaed wih opion quoed and effecive spreads. As discussed above, such analyses canno explain why he levels of spreads are so large. The only paper ha uses a large daase from he curren marke environmen, Goyenko e al (2014), separaely considers in-, a-, and ou-of-he-money opions and hus does no aemp o explain he cross-secion of spreads. We resolve he puzzle of high opion spreads by showing ha he cos of aking liquidiy in he opion marke is much less han boh he quoed spread and he convenionally measured effecive spread. These measures do no accoun for he fac ha many invesors ake liquidiy by buying (selling) opions a imes when recen sock price changes and oher high-frequency public informaion imply ha expeced changes in opion prices over very shor horizons are posiive (negaive). A large fracion of he opions rades in our sample, abou 40%, reflec such rade iming; during he las sample monh he fracion was 54%. For rades ha display high-frequency rade iming abiliy, 2 Goyenko e al (2014) use a large recen sample, while Engle and Neri (2010) use daa from nine liquid ickers in he financial secor raded in four daes of

5 an effecive spread measure ha akes accoun of i is only abou 1.3 cens per share, jus 21% of he convenionally measured effecive spread of 6.2 cens per share and 16% of he average quoed spread of 8.1 cens per share. By he las monh of he sample period he effecive spread measure ha akes accoun of rade iming abiliy is only 1.1 cens per share. These findings have sriking implicaions for he possible profiabiliy of opions rading sraegies ha involve aking liquidiy. Averaging over all rades, he effecive spread measure ha akes accoun of highfrequency rade iming abiliy is jus 67% of he average convenionally measured effecive spread and 53% of he average quoed spread. The new measure of effecive spreads declined during he sample period, beginning a 5.5 cens per share and reaching 3.5 cens per share by he end of he sample period. This decline was primarily driven by he increase in he fracion of rades ha exploi iming abiliy, which almos doubled from 27.5% o 54% of rades. A mos only a few reail invesors have he resources and abiliy o ime heir opion rades based on high-frequency changes in sock prices and oher marke informaion. Thus, our finding ha 40% of opion rades exploi abiliy o ime execuions indicaes ha a large proporion and perhaps mos opion rading is done by sophisicaed proprieary raders or insiuional invesors who eiher possess execuion algorihms or have access o brokerage firm execuion algorihms, and also sugges ha he recen growh in opion volume was driven primarily by professional invesors enering he marke. The 40% esimae is a lower bound on he proporion of sophisicaed invesors opion rades because some sophisicaed invesors will someimes rade opions wihou iming execuions. Reail and oher invesors who are no able o ime execuions will on average rade when he opion price is expeced o say he same and heir coss will equal he convenionally measured effecive spreads. During he las monh of our sample period he fracion of opion rades exploiing execuion iming had increased o 54%, indicaing ha more han half of opion rades are due o sophisicaed invesors. Our lower esimaes of he coss of aking liquidiy are driven by he fac ha a high frequencies opion price changes can be prediced using recen changes in underlying sock prices and oher high-frequency public informaion. We documen his, 3

6 and also ha many opion rades exploi his predicabiliy o rade a favorable imes. Buy rades are execued when high-frequency public informaion indicaes posiive expeced shor-erm changes in opion prices, and sell rades are execued when such informaion indicaes negaive expeced changes in opion prices. An alernaive inerpreaion is ha opion raders buy afer he value of he opion has increased o be close o he ask price bu he ask has no ye been adjused, and sell afer he value of he opion has declined o be close o he bid price bu he bid has no ye been adjused. We use wo simple models o esimae he expeced change in he opion price over shor horizons, which, combined wih he curren opion price, provide esimaes of he expeced fuure opion prices based on public informaion. The effecive spread is esimaed from he difference beween he ransacion price and an esimae of he fair marke value or underlying rue value of he securiy. 3 Convenionally, he bid-ask midpoin is used as an esimae of he securiy value, and hus he effecive spread is measured as he difference beween he ransacion price and he bid-ask midpoin. The jusificaion for his convenional approach is he lack of a readily available beer esimae of he securiy value; if a beer esimae is available, researchers should use i. We ake up he challenge of developing a beer measure of he securiy value. In paricular, we use an esimae of he expeced fuure price based on pas publicly available informaion. Because rades end o occur a imes when our esimaes of expeced fuure prices based on public informaion are sysemaically differen from he bid-ask midpoins, our esimaes of he effecive spread differ from convenional measures. The execuion iming ha we documen also resolves he puzzle of why dollar spreads of in-he-money opions are so much larger han hose of a- or ou-of-he-money opions. Opion spreads have o be wide, or else movemens in sock prices would creae arbirage opporuniies as opion marke makers ge picked off. They are wider for opions wih larger delas because he prices of such opions are more sensiive o sock price movemens. The large bid-ask spreads limi raders abiliy o exploi opion price 3 For example, he recen survey by Bessembinder and Venkaaraman (2010) explains ha he effecive spread is compued using an observable proxy for he rue underlying value of [he] securiy. In measuring price impac Hasbrouk (1991) uses he concep of he efficien price, which is defined as he expeced fuure price as he forecas horizon becomes large compued from compued from a vecor auoregression. 4

7 predicabiliy o develop profiable sand-alone rading sraegies. The large spreads also mean ha aking advanage of he shor-erm predicabiliy is a key elemen in reducing rading coss. In conras o he quoed and convenional effecive spreads, our esimaes of he coss of aking liquidiy in he in-he-money opions are no implausibly high bu raher are consisen wih he coss of execuing he iniial dela hedge rades. 4 Execuion iming also has implicaions for esimaes of price impac. Convenional measures of price impac are esimaed from he difference beween he midpoin someime afer he rade and he prevailing midpoin a he ime of he rade. We replace he midpoin a he ime of he rade wih he expeced fuure midpoin, a beer esimae of he underlying securiy value, and obain esimaes of price impac ha are only abou one-half as large as convenional measures. Our findings abou effecive spreads and price impac corroborae he growing concern ha radiional microsrucure measures do no properly capure execuion coss and price impac in modern elecronic markes (Holden and Jacobsen 2013). In addiion o corroboraing his concern, we provide measures ha ake accoun of he high-frequency predicabiliy of prices. The main resuls abou he differences in he coss of aking liquidiy are confirmed using an alernaive mehod o classify rades ino hose likely o have been iniiaed by execuion imers (algorihms) and non-imers (human raders) ha is no based on a model of fuure opion price changes. Human raders are more likely han execuion algorihms o choose round numbers (divisible by en) as heir rade size. Indeed, humans psychologically prefer round numbers (Rosch 1975), while algorihms ofen compue rade sizes using mahemaical formulas. Taking advanage of his, we use non-round and round rade sizes as proxies for rades iniiaed by algorihms and direcly by humans, respecively. 5 Trades of non-round size idenified as likely algorihmic 4 In mos cases, invesors who wish o esablish or close ou opion posiions have lile alernaive o aking liquidiy and execuion iming. For each underlying sock, opion rading is spread across up o several hundred opion conracs, mos of which rade infrequenly. As a resul, a cusomer limi order in a paricular opion is unlikely o execue wihin a reasonable amoun of ime, and opion marke-makers provide liquidiy in mos opion ransacions. 5 While his alernaive idenificaion of algorihmic and human rades does no depend on he model we use o predic opion price changes, i is consisen wih i. Our predicive model indicaes ha rades of round size (e.g., 30 conracs) are more likely o display execuion iming abiliy han rades of similar bu nonround sizes (e.g., 29 or 31 conracs). 5

8 rades have subsanially larger convenionally measured price impac han he round rades idenified as likely non-algorihmic rades. However, our price impac measure ha akes accoun of execuion iming is similar for boh round and non-round rades. This implies ha he difference in convenionally measured price impacs can be explained by execuion iming. Our resuls are imporan for inerpreing research ha documens he performance of opion rading sraegies. Recen such sudies include Goyal and Sareo (2009), Driessen, Maenhou, and Vilkov (2009), Bali and Murray (2013), Cao and Han (2013), Doran, Fodor, and Jiang (2013), Boyer and Vorkink (2014), and Muravyev (2014). The low ransacion coss obainable via execuion iming likely make profiable some rading sraegies ha would oherwise no be profiable. For example, Goyal and Sareo (2009) repor ha heir long-shor decile sraddle porfolio reurns are reduced from 22.7% o 3.9% per monh if hey assume ha opions are raded a he quoed spread, while Driessen, Maenhou, and Vilkov (2009) find ha he alpha of heir rading sraegy becomes insignifican when hey assume ha rades occur a quoed bid and offer prices. Cao and Han (2013) repor resuls for widely varying assumpions abou effecive spreads, presumably because hey have lile informaion abou he coss of aking liquidiy in he opion marke. Our finding ha coss of aking liquidiy are much less han quoed spreads and convenionally measured effecive spreads, and very much less for raders who effecively ime execuions, has implicaions for analyses like hese. We also conribue o he lieraure on opimal rade execuion (e.g., Almgren and Chriss 2001 and Bersimas and Lo 1998) by showing one mechanism ha can be used o reduce rading coss. The paper also provides a rare glimpse ino how some execuion algorihms can operae a high frequencies. 2. Daa The paper uses ick-level daa for 39 socks including 2 ETFs from he opion and equiy markes. The daa are provided by Nanex, a firm specializing in delivering highqualiy daa feeds. The sample period includes 882 rading days from April 2003 hrough Ocober The seleced socks had he larges opion rading volume during March 2003, jus prior o he beginning of he sample period. The daa include rades and bes 6

9 quoes for boh socks and opions from all exchanges which lis hem. Muravyev, Pearson, and Broussard (2013) describe he daa in more deail. Our sample period begins shorly afer he inroducion of he Opions Linkage conneced all U.S. opion exchanges in January 2003 and forced exchanges o upgrade heir infrasrucure, and was he period during which algorihmic rading came o dominae he U.S. opions markes. The period of changes in he compeiive landscape during which new opions exchanges enered he marke and almos all opions became muliply lised was compleed prior o he beginning of our sample period, and he reducion in ick sizes o pennies occurred afer he end of he sample period. Mild daa filers are applied o he rade sample. We include opions wih beween 5 and 700 calendar days before expiraion. The firs and las five minues of rading are excluded o avoid he opening and closing roaions. Trades for which implied volailiy or he expeced opion price canno be compued are also excluded. Afer applying all filers, he final sample consiss of 20.4 million opion rades. The Nasdaq ETF QQQ has he larges number of rades (1.8 million before he icker change and 1.9 million aferwards) while AOL has only 52 housand rades. 6 Summary saisics are repored in Table 1. An average rade has a price of 1.70 dollars and size of 30 conracs on hundred shares each. However, he rade size disribuion is highly skewed wih 50 h and 75 h perceniles of 10 and 20 conracs respecively; and 14% of rades have he smalles possible size of one conrac. There are slighly more seller-iniiaed rades (54%) han buyer-iniiaed rades (46%), and considerably more call opion rades (64%) han pu opion rades (36%). The rade direcion is deermined by he quoe rule. If a rade price is a he quoe midpoin of he Naional Bes Bid and Offer (NBBO), hen he quoe rule is applied o he bes quoes of he reporing exchange. The mehod is quie reliable as 84% of rades occur a he NBBO prices. On average, hree ou of six opion exchanges quoe he bes naional price a he ime of a rade. 6 AOL dropped from he sample afer changing is icker in Ocober Several oher socks also dropped from he sample due o icker changes. 7

10 3. Execuion Timing in he Opion Marke A high frequency changes in esimaes of opion values based on recen changes in sock prices predic fuure opion price changes. We firs explain our esimaes of opion values, and hen documen ha shor erm changes in opion prices can be prediced based on recen changes in he prices of heir underlying socks. Afer ha we show ha invesors exploi his predicabiliy o ime execuions of opion rades. 3.1 Esimaes of opion values implied by underlying sock prices The underlying sock price can be ransformed using he Black-Scholes-Meron (BSM) formula ino is opion price equivalen, which we call he implied opion price. We compue he implied opion price by combining he curren sock price wih implied volailiy esimaed from pas sock and opion bid-ask midpoins. The mehod consiss of wo seps oulined in Eq. (1): ˆ BSM P ˆ IV i N, (1) BSM 1 ( K, T ) BSM ( S, IV, K, T ), IV where P ( K, T ) BSM ( S, IV, K, T ) is he opion price compued using he BSM formula, S is he underlying sock price a ime, IV is he average implied volailiy over he previous hiry minues, K is he opion srike price, and T is he ime o expiraion. Specifically, for each opion we compue he implied volailiy using sock and opion bid-ask midpoins a wo-minue frequency over he previous 30 minues, i.e. a oal of N = 15 esimaes, and hen average he 15 esimaes. 7 In he second sep, he curren sock price is ransformed ino he implied opion price using he pas implied volailiy and he same BSM formula as in he firs sep. 8 Muravyev, Pearson, and Broussard (2013) use a similar idea. The mehod can be viewed as a non-linear regression beween he opion and sock prices wih one unknown parameer, he implied volailiy. The regression is esimaed on he recen price hisory and is hen used o predic he opion price corresponding o he curren sock price. Thus, he mehod depends lile on he paricular N i 1 7 The resuls depend lile on he paricular scheme used o compue implied volailiy. 8 As for he oher parameers in he BSM formula, we assume no dividends and se he risk-free rae equal o 60-day LIBOR. Time o expiraion is measured using calendar ime. The resuls change lile if we use a sock price wih one second lag o allow for possible laency beween he markes. 8

11 opion pricing model and is assumpions. However, i does require wo assumpions. Firs, i assumes ha implied volailiy changes more slowly han he underlying sock price during a rading day. Indeed, afer adjusing for marke microsrucure effecs, implied volailiy usually changes slowly and smoohly inraday. Second, he implied opion price should equal on average o he opion quoe midpoin during he esimaion window (30 minues), which is equivalen o assuming ha he opion quoe midpoin is on average an unbiased esimae of he opion fair marke value. 3.2 Shor-erm opion price predicabiliy The implied opion price is a good predicor of he change in he opion price over he nex few minues. We show his using a simple univariae regression of he change in he quoe midpoin over a horizon of lengh on he difference beween he implied opion price and he quoe midpoin, P ˆ 1( BSM P 0 P P ), (2) and hen exend he model o include oher predicors in Eq. (3) below. The model in Eq. (2) is esimaed on regularly spaced five-second inervals over each rading day, pooling ogeher all opions on a given sock. We hen average he coefficien esimaes across all rading days for each sock, and compue -saisics for he average coefficien esimaes. Table 2 repors he resuls on a sock-by-sock basis. The resuls in Table 2 show ha changes in opion quoe midpoins over each of hree ime horizons ( = 1 minue, 10 minues, and 1 hour) are prediced by he difference beween he implied opion price and he opion quoe midpoin. The implied price explains a large porion of he shor-erm variaion in opion prices, wih an average R 2 of 22% for he one-minue horizon. 9 The coefficiens range from 0.34 o 0.69, wih an average of Tha is, in jus one minue, he opion price moves more han half he disance required o converge o he implied price. As expeced, he average value of he regression coefficien is larger over he 10-minue and one-hour horizons. Alhough his simple model works well, raders who ime execuions may use addiional informaion o predic opion price changes. We find ha alhough oher 9 As expeced, R 2 decreases wih he ime horizon from 10% for he en-minue horizon o 3% for he onehour horizon. Even he laer number is large for regressions ha predic price changes or reurns. 9

12 variables somewha improve he forecass, he implied price remains he mos imporan predicor. The model P P ( Pˆ 0 1 BSM P ) ( Pˆ P ) #ExchBid BBO i i ds i i j j dp 1 4 ( ) 1 16 j #ExchAsk (3) exends he simple model in Eq. (2) and includes informaion abou he limi order book and shor-erm opion and sock price dynamics. The sae of he limi order book is represened by he difference beween he average quoe midpoin across all exchanges (BBO average) and he NBBO quoe midpoin, Pˆ BBO P. We also include he numbers of exchanges a he bes ask and bid prices wih he idea, ha if only a single exchange quoes he bes ask (bid) price, i is likely o increase (decrease) soon. Price changes over he previous minue are represened by opion and dela-adjused sock price changes over he 12 mos recen five-second periods. The regression is esimaed separaely for each sock and six groups of opions defined by absolue dela (cu-offs of 0.35 and 0.65) and ime-o-expiraion (cu-off of 60 days) on each day using regular five-second ime snapshos. Table 3 repors he average coefficien esimaes across all socks for regressions esimaed using en minue and one hour ime horizons. All of he average coefficien esimaes are highly significan and have he expeced signs. Changes in he opion quoe midpoin are highly predicable wih R 2 s ranging from 9% o 17% across he six groups a he 10-minue horizon and 8% o 18% a he one-hour horizon. The difference beween he BSM implied price and he NBBO midpoin, Pˆ BSM P, is he mos imporan variable, consisen wih he resuls in Table 2 showing ha his variable alone is able o predic changes in opion prices. The difference beween he average BBO across exchanges and he NBBO, Pˆ BBO P, is he second mos imporan variable. I is highly correlaed wih he difference Pˆ P bu also provides some independen informaion. BSM Consisen wih Muravyev e al. (2013), he opion marke lags slighly behind he underlying sock, and he opion midpoin is mean-revering perhaps because of aggressive limi orders. The role of shor-erm price swings diminishes as ime horizon increases. 10

13 We rely primarily on he exended model in Eq. (3) because opion raders who ime execuions are likely o have access o oher informaion in addiion o he sock price. However, he resuls for he round-sized rades in Secion 6 sugges ha many invesors rely only on he implied opion price in iming heir rade execuions. 3.3 Execuion iming when opion prices are predicable If he opion price changes predicably and ends o move oward he implied opion price, hen he difference beween he implied opion price and curren quoe midpoin signals he bes ime o execue a rade. Specifically, invesors who desire o buy opions should execue purchases when he implied opion price (i.e., he esimae of opion value) approaches he ask price. If hey do his hen he difference beween he ransacion price hey pay, he ask price, and he opion value will be small. Similarly, invesors who desire o sell opions should execue sales when he implied opion price approaches he bid price, because doing so will make he difference beween he value and he rade price hey receive small. We call his sraegy execuion iming. This inuiion can be generalized from he implied opion price o he general predicive model of opion price changes. The expeced fuure price from a regression aggregaes more informaion and hus is a beer esimae of he underlying opion value han he implied opion price. Specifically, he model in Eq. (3) is esimaed on pas daa, and hen he coefficien esimaes are muliplied by curren values of he covariaes o produce he prediced opion price a a given horizon (e.g., one hour). This prediced price can be used in he same way as he implied opion price: if he price is expeced o increase (decrease), hen i is good ime o buy (sell). Figure 1 is a sylized illusraion of execuion iming. The figure shows opion prices (verical axis) evolving in ime (horizonal axis). The expeced fuure midpoin (i.e., he opion value) is shown in green. I evolves over ime as he sock price, which is no shown, also evolves. We assume ha he curren quoe midpoin (grey) evenually converges o he fuure expeced midpoin (green) implied by he curren price of he underlying. Execuion imers will wai unil he expeced quoe midpoin approaches he bid price (dark blue) o execue heir sell rades, indicaed by solid blue arrows. In his illusraion invesors imed heir sales well because if hey had waied longer he bid price hey receive would have decreased. 11

14 This example also illusraes why convenional measures of he bid-ask spread and price impac ha use he curren quoe midpoin overesimae rading coss. Because he convenional measure of he effecive spread uses he quoe midpoin, i assumes ha he sell rades in he figure incur he same coss as hypoheical buy rades execued a he same ime. However, such buy rades are a poor rading decision because he invesor could have waied for he expeced decrease in price o ake place and hen buy a a beer price. Tha is, he convenional measure of he effecive spread fails o accoun for price predicabiliy. More specifically, when he sell rades occur he curren quoe midpoin is above is expeced fuure value, which is he esimae of opion value. Using he higher curren quoe midpoin as a proxy for he opion value oversaes he effecive spread and price impac of he rade. The quoe midpoin is on average significanly higher han is expeced value a he ime of sell rades, and price will decrease even if no sell rades occur. Figure 2 uses he daa o show ha invesors do in fac acively engage in execuing iming: hey buy righ before he price is expeced o increase and sell before i is abou o decrease. The red line shows he prediced change in opion price based on public informaion immediaely before a rade compued using Eq. (3) wih a 10-minue horizon. The prediced change is ploed as a funcion of he signed rade size, in dollars. For posiive signed rade sizes he opion price is expeced o increase by approximaely one cen, ranging from slighly below one cen for small rades o slighly above one cen for large rades. Following negaive signed rades he expeced opion price change ranges from 0.5 cens o almos 1.5 cens, wih he price change being abou 1 cen for much of he range of rade sizes. The blue line shows he opion price changes during he 10 minues following a se of simulaed rades for he same opion and dae a random imes ha do no overlap wih he 10 minues periods following he ime of an acual rade. As expeced, he average opion price changes following hese rades are close o zero. The difference beween he red and blue lines is due o execuion iming. The green line shows he change in he opion price midpoin from he ime of a rade unil 10 minues afer he rade. The prediced price change condiional on a rade (he red line) has he same sign as he acual change (he green line) bu is smaller 12

15 because no all raders ime execuions and because opion prices change due o invenory and adverse-selecion impacs as discussed furher in Secion Wha fracion of rades reflecs execuion iming? The difference beween he expeced fuure price from he regression model, and he curren quoed price,, compued for each rade and adjused for he rade direcion, is a measure of execuion iming (ET). We normalize he difference by he effecive bid-ask half-spread a he ime of a rade o express he benefis of he execuion iming as a percenage of one measure of rading coss. The following equaion summarizes he definiion: ( Pˆ, i P, i ) I buy/sell ETi Effecive Bid Ask Spread,i / 2, (4) where I buy/sell = 1 if he ih rade is buyer-iniiaed and 1 if i is seller-iniiaed. The larger he execuion iming measure is for a rade, he more likely i is iniiaed by a rader who imes execuions. This measure provides a lower bound esimae for he exen of execuion iming. Alhough our regression model capures he firs-order variaion in he expeced price changes, some invesors may develop a beer predicive model. In his case, a beer model will find opporuniies o rade a low coss ha a simpler model will miss. Tha is why, similarly o he quoe midpoin versus he implied price case, he expeced price for a beer model will be sysemaically above he one from a simpler model for buyeriniiaed rades. Using his measure, we can esimae he share of rades iniiaed by execuion imers. While execuion imers submi heir buy (sell) rades when he expeced change in price is posiive (negaive), for oher raders who do no ime execuions he price is expeced o say he same on average. We use he idea ha hese oher raders have zero execuion iming o esimae he marke share of execuion imers. Indeed, assuming ha execuion imers do no rade when he expeced change is negaive, all he rades wih negaive iming are iniiaed by ohers. If he disribuion for he expeced price changes for oher rades is symmeric around zero, hen he disribuion can be reconsruced as a mirror reflecion of he negaive par which is observed. Thus, he oal number of rades 13

16 no reflecing execuion iming is simply wice he number of rades wih negaive iming. Subracing his quaniy from oal number of rades, we can obain an esimae of he number of rades reflecing execuing iming. Thus, marke share of rades reflecing execuion iming can be compued wih he following formula: Share of Execuion Timing 1 2 I ET i 1, (5) Toal Number of Trades where I A is an indicaor funcion for he se A. Using his approach, we esimae ha share of rades iniiaed by execuion imers increased from 27.5% a he sar of our daa period in April 2003 o 54% in lae 2006 as repored in Figure 3 and Table 4. These percenages can be considered lower bounds on he amoun of algorihmic liquidiy aking in he opions marke because no all algorihmic liquidiy aking will reflec execuion iming. This resul implies ha by he end of our sample mos of he rades are originaed by sophisicaed raders such as proprieary rading firms, hedge funds, and insiuional invesors who eiher have heir own execuion algorihms or have access o brokerage firm execuion algorihms. Alhough he idea underlying execuion iming is simple, only hese invesors have access o he echnology needed o implemen i. The esimaed fracion of execuion imers provides a lower bound for he fracion of such invesors in he opions marke because he inheren limiaions of he regression model cause i underesimae he prevalence of execuion iming and because some sophisicaed invesors do no ime execuions of some or all of heir opion rades. Overall, hese esimaes are inconsisen wih a common view ha reail invesors are responsible for mos of opion rading, and also sugges ha he recen growh in opion volume was driven primarily by professional invesors enering he marke. 4. Biases in Measures of Execuion Coss and Price Impac This secion shows how convenional measures sysemaically oversae opions rading coss and esimaes of price impac when prices change predicably and opions invesors engage in execuion iming 4.1 Effecive spreads 14

17 Theoreical lieraure emphasizes ha measures of rading coss should rely on he bes esimaes of securiie s fair marke values. The expeced fuure price from he regression model is he bes linear esimae of his kind and hus should be used. However, he empirical lieraure overwhelmingly uses he curren quoe midpoin insead of is expeced fuure value, implicily assuming ha price changes are unpredicable. Alhough he quoe midpoin is a less precise esimae of he opion value han he expeced fuure quoe midpoin, his does no creae any bias if raders have no or limied abiliy o ime execuions. Indeed, he quoe midpoin a a random momen is equal on average o is fuure value. However, he siuaion differs in markes in which i is possible o ime execuions. Alhough he quoe midpoin a a random momen is unbiased, i is biased a he ime of a rade by a rader who imes execuions. As a resul, convenional ex-ane measures of he bid-ask spread oversae rading coss. This bias can be correced by replacing he quoe midpoin wih is expeced fuure value from a regression model, i.e. he usual effecive spread measure 2 / is replaced by he adjused effecive spread 2 /, where TP is he rade price a ime and Pˆ he midpoin a ime +. is he esimae of Consider an example. Suppose ha a call opion is rading a 1.0/1.1 dollars bid/offer, and he quoe midpoin is expeced o increase by 1 cen in he nex minue from 1.05 o 1.06 dollars. An invesor wans o buy a he ask price because he price is abou o increase. The convenional measure of he effecive half-spread for his rade is 5 cens ( ), while he acual cos as measured by he adjused effecive halfspread is only 4 cens ( ). Table 5 repors differen rade-weighed measures of he spreads for each sock in our sample, along wih he averages across socks (a he op of he able). 10 The column headed Avg. Quoed repors he average daily quoed spreads based on he NBBO. This average is compued by assigning o each opion rade he average quoed spread for he day, where he quoed spreads are compued separaely for each opion from one- 10 The overall average spread measures in his able differ from hose in Table 4 due o a difference in he way he averages are compued. The average spreads in he firs row of Table 5 are averages across socks, where each sock is weighed equally. The average in Table 4 are across monhs, and do no include he socks ha dropped from he sample in he monhs afer he socks dropped. 15

18 second snapshos on each day. These reflec rading coss for an invesor who rades a random imes. 11 The overall average of 8.4 cens in he firs row indicaes ha such an invesor pays 8.4 cens for a round-rip rade or 5 percen of an average opion price of 1.70 dollars. Invesors can reduce he coss by rading when he quoed spread is narrower, and rades end o occur when quoed spreads are less han average. The column headed Average Quoed a Time of Trade shows ha he average quoed spread a he ime of a rade is 6.6 cens per share. The average effecive spread in he nex column is he doubled difference beween he rade price and he quoe midpoin. I is jus a bi smaller, 6.4 cens per share, reflecing he fac ha occasionally rades occur inside he quoed spread, hough his is no frequen as more han 80% of opion rades are execued a he NBBO quoes. The nex column shows he average realized spread. The nex wo columns headed Adjused, BSM and Adjused, Regression show adjused effecive bid-ask spreads based on he simple regression model using only he difference beween he BSM implied opion price and he quoe midpoin (Eq. 2) and he more general regression model (Eq. 3), respecively. The adjused-effecive bid-ask spread is wice he difference beween ransacion price and he expeced price implied by he predicive model. The overall average esimae of he adjused effecive spread based on he regression model in he column Adjused, Regression is 4.5 cens, which is 30% less han he convenionally measured effecive spread and 46% less han he average quoed spread. The spread compued using he BSM implied opion price is even smaller, 4.2 cens, which is only half of he quoed spread. The execuion iming affecs no only he level of rading coss bu also he relaive sock ranking. For example, Pfizer and QLogic have he same adjused-effecive spreads of 4.3 cens, bu very differen quoed spreads of 7 and 9.8 cens. These resuls indicae ha opion rading coss are much lower han indicaed by eiher quoed or convenionally measure effecive spreads. Execuion iming is essenial for rade execuion and significanly reduces rading coss. Furher, hese resuls are based on all rades, including rades execued by invesors who do no engage in 11 The lieraure mosly uses he end-of-he-day bid-ask spread from OpionMerics, which is a special case of he average quoed spread wih only one observaion per day. 16

19 execuion iming. The execuion coss of raders who are able o ime execuions are lower sill. The role of he execuion iming increased subsanially during he sample period as execuion algorihms improved and heir share increased. Figure 4 shows ha he adjused effecive spread decreases from 6.5 cens o 3.5 cens while he average quoed spread remains approximaely unchanged a abou 8 cens, and he effecive spread modesly decreases from 7.5 o 6 cens. Thus, he adjused-effecive spread decreases by almos half while he convenional spreads change lile. Several ime-series properies of he average spreads are worh noing. Alhough rading coss for any paricular sock are quie volaile, heir marke average flucuaes in a narrow range. Thus, rading cos volailiy seems o be diversifiable a leas during normal imes. The average spreads follow a long-erm rend and display lile volailiy clusering. The adjused effecive spread is similar o he realized spread, wih he difference being ha he realized spread uses he acual pos-rade midpoin raher han he esimae. However, i has several advanages over he realized bid-ask spread. Firs, he adjused spread is an ex-ane measure ha can be used for rade execuion. Second, he realized spread reflecs no only rading coss bu also he informaion and invenory impacs of a rade making i hard o disenangle hese effecs, while he adjused spread only measures rading coss. Finally, he realized spread provides a more volaile esimae of rading coss because fuure price is more volaile han is forecas. 4.2 Measures of Price Impac Prices respond o rades swifly and by large amouns. The wo columns of Table 6 headed Observed Price Impac, Cens show he convenional price impac measures / for he various socks in our sample using horizons of one and en minues. The averages for he wo differen horizons across socks are shown in he firs row of he able. These resuls show ha, on average, he quoe midpoin moves by 1.13 and 1.34 cens in he firs one and en minues afer a rade, which is large relaive o he $1.70 average opion price. However, convenional measures of price impac significanly overesimae he causal effec of rades on prices, for he same reason ha convenionally measured 17

20 effecive spreads do. Eq. (6) decomposes he observed price impac ino he correcly measured price impac of a rade, and he expeced change in he quoe midpoin if no rade occurred: 12 P P Observed Price Impac ˆ P P Price Impac ˆ P P (6) Expeced Price Change Furher decomposing he price impac ino componens due o asymmeric informaion and invenory risk, we obain P P Observed Price Impac ˆ ˆ AI P P ) IR ( P P ) Asymmeric Informaion Invenory Risk ˆ P P (, (7) Expeced Change where 1 In he opions marke, he expeced price change is of roughly he same magniude as he correcly measured price impac of a rade if one uses a shor horizon of one minue and is larger han he correcly measured price impac if one uses a horizon of en minues. Specifically, in Table 6 he pair of columns headed Observed Price Impac repor esimaes of convenionally measured price impacs for horizons of one and en minues for each of he socks in he sample, as well as he averages across socks. The pair of columns headed Expeced Price Change and Ajused Price Impac repor esimaes of he expeced price changes and correcly measured adjused price impacs for each of he socks in he sample for he same horizons. For he one minue horizon he average expeced price change is 0.47 cens, which is 42% of he convenionally measured price impac of 1.13 cens, and he correcly measured adjused price impac is only 0.66 cens, or 58% of he convenionally measured price impac. For he 10 minue horizon, he average expeced price change is 0.82 cens, which is 61% of he convenionally measured price impac of 1.13 cens, and he correcly measured adjused price impac is only 0.52 cens, or 39% of he convenionally measured price impac. (In unabulaed resuls using only he BSM implied opion price wih Eq. (2) we find ha even wihou a rade he quoe midpoin would move by 1.08 cens over he 10-minue horizon, which is 81% of he observed price impac of 1.34 cens.) Thus, alhough i is 12 Price impac is adjused for he rade direcion everywhere in he paper. The expeced par is esimaed from a predicive model bu wih a smaller ime horizon (for example, en minues) han commonly used in price impac measures. 18

21 emping o aribue he large convenionally measured price impac o informed rading, in fac, over a horizon of 10 minues he expeced price change consiues he majoriy of he convenionally measured price impac. The addiional decomposiion in Eq. (7) makes clear ha he expeced price change is large relaive o he effecs of boh asymmeric informaion and invenory risk. How price impac changes wih rade size is of paricular ineres for idenifying informed rading. Figure 6 shows he convenionally measured price impac exceeds one cen even for small rades. I is increasing for small rades and is almos fla (a approximaely wo cens) for rades of more han hiry conracs. Bu he mos pronounced paern, which is discussed in Secion 6, is ha rades of round (divisible by 10) sizes have significanly lower (by half a penny) price impac han non-round rades. To idenify he causal impac of rades on prices he observed price impac should be adjused by subracing he expeced price changes. These adjused price impacs based on boh he regression and BSM models are shown in Figure 7. Using he regression model, he adjused price impacs are much smaller and now increase seeply wih rade size. The BSM-adjused price impacs are even smaller, and have many desired properies. They sar almos from zero as rades of one conrac have an adjused price impac of only 0.07 cens. The BSM-adjused price impacs increase monoonically o abou 0.6 cens. Also, as discussed in Secion 5, he differences beween he price impacs of round and non-round rades disappear. We use regression analyses o sudy how he observed and adjused price impacs depend on rade characerisics. The firs hree columns in Table 7 shows he resuls from hree differen regressions of he observed price impac over a en minue horizon following he rade on a number of variables, including he absolue value of he opion dela ( ), he square roo of he ime o opion expiraion ( 19 T ), a dummy variable aking he value of one if he opion raded is a call (I Call ), a ime rend measured in years (TimeTrend), he opion bid-ask spread measured in cens (Bid-Ask), a dummy variable aking he value of one if he rade is a purchase (I Buy ), he square roo of he rade size measured in conracs ( Size ), a dummy variable aking he value one if he rade size is one conrac (I Size = 1 ), he number of opion exchanges a he NBBO on he side of he marke where he rade occurred (#ExchANBBO), a dummy variable aking he value

22 one if here is only one exchange a he NBBO on he side of he marke where he rade occurred (I #Exch = 1 ). Two of he specificaions also include he prediced price change from he regression model, Pˆ, and one of he specificaions includes dummy variables aking he value one if he expeced quoe change based on he regression model is beween zero and wo cens, wo and five cens, and greaer han five cens ( ˆ P I, 0 x 2 ˆ P T I 2 x 5, and P I5 x ˆ any of he expeced price change variables, respecively). In he firs specificaion ha does no include Pˆ, ˆ P I 0 x 2, ˆ P T I 2 x 5, or Pˆ I5 x he mos imporan variables are he wo variables #ExchANBBO and I #Exch = 1 describing he sae of he opions limi order book. The coefficiens of and on hese variables indicae ha for buy (sell) rades, he price impac decreases (increases) by cens wih each addiional exchange a he ask (bid) price and increases (decreases) by cens if a single exchange quoes he bes ask (bid) price. Turning o he oher coefficien, he ime rend is very srong: he observed price impac increases by 0.55 cens each year. Price impac is increasing in rade size, bu he impac of a rade of 100 conracs is only cens. The coefficien for he level of he opion price is small (0.158), validaing our approach of measuring opion price impac in dollar erms. The second column repors he resuls of a specificaion ha also includes Pˆ, he prediced price change from he regression model. The esimaed coefficien on his variable is large, 0.776, and highly significan (-saisic = 66.92), confirming ha much of he convenionally measured price impac is explained by he expeced price change based on public informaion. 13 Including his variable in he regression has imporan impacs on many of he oher regression coefficien; for example, he coefficiens on he variables #ExchANBBO and I #Exch = 1 describing he sae of he opions limi order book change from o and from o 0.194, respecively. The hird column also includes he variables ˆ P I 0 x 2, ˆ P T I 2 x 5, or Pˆ I5 x ha capure nonlineariies in he relaion beween he observed price change and he regression-based 13 In a univariae regression ha includes only his variable is Pˆ on he righ-hand side he esimaed coefficien on 20

23 forecas of he price change. The esimaed coefficiens on hese variables are highly significan, and he coefficien on Pˆ is reduced o The fourh column repors resuls for a specificaion in which he lef-hand side variable is he BSM-adjused price impac P Pˆ. Srikingly, for he BSMadjused price impac, mos of he coefficiens on he independen variables become much smaller in magniude and he R 2 drops o zero. For example, he coefficien on he 21 BSM number of exchanges a he NBBO, #ExchANBBO, decreases from in he firs specificaion o 0.058, and he coefficien on I #Exch = 1 decreases from o and becomes insignifican. These observaions ogeher wih he analysis of round and non-round rades in Secion 6 are consisen wih he hypohesis ha opion markemakers and algorihmic raders ime execuions using he BSM model or a similar approach. 4.3 Effecive spreads of raders who do and do no ime execuions We now urn o esimaing he spreads of liquidiy-aking rades ha do and do no reflec execuion iming and examining how hey changed during our sample period. Our approach o esimaing he spreads of liquidiy-aking rades ha do and do no reflec execuion iming is based on he auological assumpions ha (a) liquidiyaking rades execued by raders who ime execuions have non-negaive execuion iming, and (b) liquidiy-aking rades by raders who do no ime execuions have no execuion iming abiliy. We used hese assumpions above o idenify he shares of liquidiy-aking rades by execuion imers and non-imers. In paricular, each rade is assigned a probabiliy of being iniiaed by an execuion imer. Our approach consiss of wo seps. Firs, we recover he empirical disribuion of execuion iming for he liquidiy-aking rades ha do no display execuion iming. The second assumpion (b) implies ha he average execuion iming should be zero or close o zero and is disribuion should be symmeric around zero in a large sample of rades by raders who do no ime execuions Thus, only rades by raders who do no ime execuions can have non-posiive execuion iming. We use his subsample of rades wih non-posiive iming o infer he lef half of he probabiliy disribuion for he execuion iming of nonalgorihmic raders. Because he disribuion is symmeric, esimaing is lef side is