Execution Timing in Equity Options

Transcription

1 Execuion Timing in Equiy Opions Dmiriy Muravyev Boson College Neil D. Pearson Universiy of Illinois a Urbana-Champaign [Preliminary Draf: Please do no cie or circulae wihou he auhor s permission] Absrac Convenional measures of rading coss rely on he quoe midpoin as an esimae of he rue securiy value. However, invesors employ a more precise esimae, which akes advanage of public informaion besides bes quoes. Invesors buy when heir public informaion midpoin is close o he ask price and herefore is above he quoe midpoin. As a resul, convenional measures have a subsanial upward bias, which is paricularly large in he opions marke. The effecive and average quoed spreads overesimae acual rading coss by 42% and 87% respecively; or by several billion dollars annually. The iming bias varies across socks and grew dramaically larger over ime. Trades of non-round size pay smaller spreads. Trades cause only smaller par of he observed price impac, while expeced changes in he quoe midpoin is he dominan componen. Convenional measures can be adjused for he iming bias. Our resuls indicae ha he adjused measures should be used o make inferences abou liquidiy and informed rading. Keywords: Bid-ask spreads, price impac, algorihmic rading, public informaion, liquidiy, equiy opions. We graefully hank Nanex and Eric Hunsader for providing he rade and quoe daa for he opions and heir underlying socks. Dmiriy Muravyev acknowledges financial suppor from he Irwin Fellowship a he Universiy of Illinois. addresses: muravyev@bc.edu (D. Muravyev), pearson2@illinois.edu (N. D. Pearson)

2 Inroducion If he quoe midpoin is replaced wih a more precise measure of fair value based on a wider se of public informaion, will i make a difference? We show ha i will because convenional measures based on he quoe midpoin significanly overesimae rading coss and price impac. Alhough he quoe and public informaion midpoins are equal on average, hey differ sysemaically a he ime of rades. Invesors buy when he public informaion midpoin is close o he ask price and herefore is above he quoe midpoin, as Figure 1 illusraes. Thus, he convenional bid-ask spreads are larger han acual rading coss. The daa reveal ha invesors and heir execuion algorihms rely on he public informaion midpoin, academics should follow sui. Measures of rading coss and price impac play a fundamenal role in financial economics. An analysis of permanen and emporary price impacs sheds ligh on informaion flows wihin and beween markes 1. The link beween liquidiy and asse reurns receives increasing aenion, wih he bid-ask spreads being he mos popular measure of liquidiy 2. Realisic esimaes of rading coss are required o access an economic magniude of rading sraegies which es marke efficiency. Tradiional measures of rading coss universally rely on he quoe midpoin as an esimae of he rue value. 3 This assumpion has hisorical roos as ousiders ofen had access only o he bes bid and ask prices. However, currenly, invesors can easily access a considerable amoun of public informaion besides bes prices, wih limi order book and prices of relaed securiies being he mos obvious examples. The public informaion allows for a more precise esimae of he rue securiy value 4 han he quoe midpoin, which we call he public informaion midpoin (or simply he public midpoin). More specifically, he public midpoin is defined as he bes 1 Hasbrouck (1991) is a good example. 2 Amihud, Mendelson and Pedersen (2006) provide an exensive survey. 3 For example, he effecive bid-ask spread is defined as a doubled difference beween he rade price and he quoe midpoin a he ime of he rade. Bessembinder and Venkaaraman (2009) and numerous oher papers have his definiion. 4 We define fair value as a marke consensus abou a price of a given securiy. Mos of he ime he fair value is beween he bes bid and ask prices, oherwise invesors will rade agains hem. 1

3 forecas of he fuure quoe midpoin based on he curren quoe midpoin and oher public variables, as summarized by Equaion (1) 5. ( P P, X ) ˆ + = (1) P T E + T 0, We argue ha he quoe midpoin should be replaced wih he public midpoin in all measures of rading coss and price impac. For example, Equaions (2) and (3) show how he effecive bid-ask spread becomes he public effecive spread (or simply he public spread) afer he adjusmen. Alhough heoreical lieraure acknowledges he imporance of accouning for public informaion in esimaing he rue securiy value, empirical lieraure almos universally ignores 6 his recommendaion. Coss= 2(TradeP - P ) Coss= 2(TradeP - Pˆ ) (2) + T Impac = + P Impac= + + T + T P Pˆ Pˆ (3) The adjused measures are imporan because, besides being more accurae, hey reflec how invesors acually execue rades 7. The main way o minimize rading coss is he sraegy called he execuion iming. Invesors ime heir purchases o he momens when he public midpoin is close or above he ask price. Thus, he public midpoin is sysemaically above he quoe midpoin a he ime of buyer iniiaed rades. As a resul, convenional measures based on he quoe midpoin overesimae rading coss creaing he execuion iming bias. If invesors were execuing rades a random, here would be lile difference beween he convenional and adjused measures. However, invesors ime heir rades. The execuion iming implies ha convenional measures of price impac also have an upward bias. These measures usually don accoun for he expeced changes in he quoe midpoin. If he public midpoin is much higher han he quoe midpoin, he laer will increase converging o he former. A he same ime, execuion algorihms are likely o buy because he public spread is relaively small. As a resul, Figure 1 shows ha only a porion of he subsequen increase in he quoe midpoin should be aribued o he causal impac of rades, he remainder is simply regression oward he mean. 5 Equaion (1) is linear, bu non-linear models can poenially improve he forecas. 6 Hasbrouck (1991) is one of few excepions. He conrols for pas price changes and signed volumes o disinguish he permanen and ransiory price impacs. However, oher public variables are no included. 7 Unlike pos-rade measures, pre-rade measures no only esimae coss bu also ell when o rade. 2

4 Imporanly, he invesor s abiliy o buy before he price increase is based on effecive processing of public raher han privae informaion. Empirical par of he paper demonsraes ha he execuion iming bias is large in he opions marke. The effecive and average quoed spreads overesimae acual rading coss by 42% and 87% respecively! The opions marke is a perfec laboraory o sudy he iming bias for wo reasons. Firs, he underlying sock price is obviously he mos imporan public informaion for opion prices. Second, he Black-Scholes-Meron model (BSM) provides a common way o ransform he underlying price ino he implied opion price 8. Thus, he model selecion is much easier for opions han for socks. In addiion o his simple model, we also employ a regression model in he spiri of Equaion (1). I predics changes in he opion midpoin based on he BSM implied price and informaion abou opion limi order book and shor-erm price dynamics. We apply hese wo mehodologies o he sample of opions on 39 socks over he hree-year period from April 2003 hrough Ocober 2006, and find several implicaions of he execuion iming. Firs, as menioned above, boh rading coss and price impac have much smaller magniudes han was previously believed. In absolue erms, he execuion coss are overesimaed by several billion dollars per year 9. Second, here is a subsanial variaion in he iming bias across socks. Thus, convenional and adjused measures of he bid-ask spread can rank socks differenly. Third, he magniude of he execuion iming bias increased hreefold in less han four years. The execuion iming will be even more imporan in he fuure. This finding demonsraes he profound effec of he growh in algorihmic rading on he opions marke. Finally, he execuion bias varies wih rade size. Trades of round size, divisible by 10, have subsanially worse execuion and smaller price impac han non-round rades 10, while he effecive spreads are he same for wo groups. The round-volume resuls shed ligh on he execuion iming model used by a represenaive execuion algorihm. 8 An addiional assumpion is ha curren opion quoe midpoin will evenually converge o he BSM implied price. 9 Indeed, combining opion rading volume of 4.6 billion conracs in 2011 wih average execuion bias of 2 dollars per conrac produces a muli-billion dollar number. Each opion conrac is on one hundred shares. hp:// 10 For example, rades of 30 conracs pay a spread of four cens, while rades of 29 or 31 conracs pay only hree cens. 3

5 The paper raises an imporan policy quesion concerning he proecion of reail invesors. Currenly, reail invesors cross-subsidize insiuional raders 11 by paying he enire bid-ask spread while insiuional algorihms employ he execuion iming and pay only half of i. Marke makers effecively quoe a differen spread for each of he wo invesor ypes. Informaion is largely symmeric, and marke makers can esimae he probabiliy of a rade coming from each invesor ype condiional on he public midpoin. The main fricion is ha reail invesors canno consanly re-compue and updae heir quoes. This fricion can be elevaed by delegaing his funcion o he broker or exchange level. One possible soluion is o quoe opion prices in implied volailiy raher han dollar erms. A less radical soluion would be o encourage exchanges o inroduce limi orders linked o implied volailiy 12. Overall, our resuls indicae ha he usage of he adjused measures is crucial for making inferences abou liquidiy and informed rading. The execuion iming provides exciing insighs abou he inner workings of algorihmic rading. Daa The paper employs ick-level opion and sock daa on 39 socks including 2 ETFs. The daa are provided by Nanex, a firm specializing in delivering high-qualiy daa feeds. The sample period is April 2003 hrough Ocober 2006 and includes 882 rading days. The seleced socks had he mos liquid opions as measured by rading volume prior o he beginning of he sample period in March The daa include rades and bes quoes for boh socks and opions for all exchanges. A more deailed descripion of he daa is provided by Muravyev, Pearson, and Broussard (2012) 13. We include only opions wih beween 5 and 700 calendar days before expiraion. Firs and las five minues of a rading day are excluded o avoid opening and closing roaions. Trades for which implied volailiy or he public midpoin canno be compued are also excluded. 11 If dealers are compeiive and make zero profis, profis of one invesor group equal o losses for he oher. 12 This soluion may pose echnical challenges because quoe raffic will increase. 13 Compared o Muravyev e al. (2012), we exclude DIA because hrough mos of he sample period i was raded only a CBOE. 4

6 The paper sudies of opion rades and subsequen quoe changes. Tables 1 and 2 summarize main descripive saisics. The oal sample includes 20.4 million opion rades. Nasdaq ETF QQQ/QQQQ 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 14. Average rade ransacion has a price of 1.7 dollars and size of 40 conracs 15. 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 (54%), and call opion ransacions (64%). The direcion of a rade is deermined by he quoe rule. If a ransacion price is a he Naional Bes Bid and Offer (NBBO) quoe midpoin, he quoe rule is applied o he bes quoes of he exchange which repored he ransacion. As 84% of ransacions are recorded a NBBO prices, he mehod is easy o apply. On average hree ou of six exchanges are quoing he bes naional a he ime of rades. Mehodology Time is money by posponing rade execuion, invesors can lower rading coss. Bu how exacly can invesors achieve his? Alhough here is a large heoreical lieraure on opimal rade execuion, no much is known abou inner workings of he black box of algorihmic rading 16. We show ha he execuion iming is one of he mos effecive ways o minimize rading coss. As Figure 1 and Equaions (1)-(3) imply, he model for he public midpoin plays a key role for he execuion iming. In he firs sep, variables represening public informaion and a funcional form are seleced for he main regression in Equaion (1). Then, he regression coefficiens are esimaed on he sample from regular ime inervals 17. Finally, he coefficiens are employed o esimae he public midpoin a he ime of rades. 14 AOL dropped from he sample afer changing is icker in Ocober Each opion conrac is on one hundred underlying shares. 16 The convenional wisdom is o spli large rades o minimize emporary price impac. Anand e al. (2012) sudy rade execuion coss for he daabase of insiuional rades. However, hey have no informaion on how broker s execuion algorihms work. 17 Trade iming is endogenous, ha is why regular ime inervals are appropriae. 5

7 Ideally, all public informaion should be included in he main regression. However, i s hardly feasible because some public informaion is cosly o acquire 18, and hisorical daa are ofen no available. Despie his difficuly, i is ofen possible o idenify firs order variables from general consideraions. For example, for he sock marke he mos relevan variables include price hisory, sae of he limi order book, and marke and indusry componens. Saisical mehods of model selecion can help wih picking specific variables. For he opions marke he ask is much easier as he underlying sock price is clearly he main public informaion. The model specificaion is also easier o choose for he opions marke as he Black-Scholes-Meron formula links opion and sock prices. Afer he public midpoin model is esimaed, he adjused measures of he bid-ask spread and price impac in Equaion (3) can be compued. If here are several alernaive models, he mos precise one should be chosen. The adjused measures can subsanially reduce bu canno fully eliminae he iming bias. Having beer resources, sophisicaed invesors can poenially selec a beer public midpoin model han academics 19. Thus, our esimaes provide a lower bound for he execuion iming bias. Indeed, a more precise model will find opporuniies o rade a low coss ha a simpler model will miss. Similar o he public versus quoed midpoin case, he public midpoin for a sophisicaed model will be sysemaically above he one from a simple model for buyer iniiaed rades. Pˆ + T P = E E ( P P P, X ) + T 0, P P X 0, ( Pˆ Pˆ X ) = 0 + T 6 0, Imporanly, Equaion (1) serves primarily as a ool o esimae he difference beween public and quoed prices a he presen momen raher han o forecas fuure price dynamics. Indeed, Equaions (4) show ha if he quoe midpoin will converge o he public one wihin ime T 20, hen he prediced change in he quoe midpoin equals o he curren difference beween he wo midpoins. Time T in he formula should be large enough for he quoe midpoin convergence. The convergence can ake more han an hour in he opion marke mainly because of he large bid-ask spreads. 18 Grossman and Sigliz (1980) 19 The model can be non-linear such as neural neworks. 20 An addiional assumpion is ha he public midpoin follows a maringale. ˆ (4)

8 The predicable behavior of he quoe midpoin is consisen wih he efficien marke hypohesis, since he expeced profiabiliy is smaller han rading coss and risks. Indeed, he public midpoin is normally wihin he bid and ask prices. The execuion iming is used o minimize rading coss raher han o make arbirage profis. To quanify he effec of he execuion iming for any given ransacion, Equaion (5) defines a measure of he execuion iming bias as one minus he raio of he public o effecive spreads. As he public spread is wice he difference beween he ransacion price and he public midpoin, he iming bias can be rewrien in erms of he difference beween he public and quoe midpoins normalized by a bid-ask spread. Timing Bias Public Spread = 1 EffeciveSpread Pˆ + T P = BidAskSpread As discussed above, convenional measures of price impac significanly overesimae he causal effec of rades on prices. To remind he mechanism, invesors buy when he public midpoin is close or above he ask price. A he same ime, he quoe midpoin will increase converging o he public midpoin. Equaion (6) decomposes he observed price impac 21 ino is causal impac, and he expeced change in he quoe midpoin if here were no rade. The expeced par is esimaed wih Equaion (1) bu wih smaller ime horizon han for he public midpoin. Price impac is radiionally esimaed over ime horizon of one o weny minues ha may no be enough for he quoe midpoin o converge o he public midpoin. P P Observed Price Impac / 2 ˆ + + T ˆ + + T ˆ + T ˆ + T = P + P + + P + P + P P (6) 0 for large Public Price Impac Timig Bias The execuion bias in price impac has several implicaions. Firs, price impac is commonly decomposed ino asymmeric informaion (privae informaion) and invenory risk componens 22. This paper inroduces he hird componen, he expeced quoe changes based on he available public informaion. The execuion iming componen plays a leas as imporan as he oher wo. In addiion, he iming bias in price impac has differen magniude for differen subses of rades. For example, he bias is higher for large rades because hey are more (5) 21 Price impac is adjused for rade direcion everywhere in he paper. 22 See Muravyev (2011) for a recen example. 7

9 likely o come from sophisicaed invesors. Thus, he slope of he price impac as a funcion of rade size is genler han is implied by convenional measures. Las par of he paper ries o reverse engineer he public midpoin model of a represenaive invesor. If wo groups of rades have equal asymmeric informaion and invenory risk, hen he difference beween heir price impacs is enirely due o he execuion iming 23. The simples model for he public midpoin relaive o which he difference in price impacs disappears is he model used by a represenaive algorihm. Indeed, if invesors use a facor which is omied from he model, hen he adjusmen for he expeced change in he quoe midpoin 24 won fully eliminae he difference in price impacs. On he oher hand, if he wo groups differ in heir privae informaion conen, hen he difference in price impacs will remain under any model. The difference in he group price impacs provides a model free lower bound for he execuion bias as boh groups conain some execuion iming. If he difference is significan, i helps o eliminae concerns abou he iming bias being mechanically produced by a public midpoin model. The wo groups of rades we choose are round versus non-round sized rades. Round rades are rades of more han fifeen conracs, wih size divisible by en and o a lesser degree rades divisible by five. The comparison can be done separaely for each round number or joinly. The non-round rades have larger iming bias because hey are more likely o come from sophisicaed invesors employing algorihmic rading. Firs, for psychological reasons, unsophisicaed invesors are likely o choose a round number as a arge posiion, and o acquire i in a single ransacion. On he oher hand, sophisicaed invesors are more likely o compue he arge posiion from a model 25. Second, execuion algorihms are likely o spli he arge size ino muliple rades o ake advanage of opporuniies. If he price is aracive, hey will ake all he available size a i. Empirically, sophisicaed invesors use non-round rades for boh reasons, bu aking all available size a aracive price is more imporan. 23 For example, he proporion of noise raders is differen for he wo groups. 24 The expeced change in quoe midpoin can be approximaed by he difference beween he quoe midpoin a he end of he period and he curren public midpoin. 25 For example, exoic derivaives desks commonly hedge wih plain vanilla opions. 8

10 Invenory risk is he same for he wo groups because here is lile difference in rade size. Compare for example 29 and 31 wih 30 conracs. Marke makers may hink ha non-round rades are more informed and reac o hem more. However, privae informaion conen of rades is no observable which makes i hard o es he proposiion empirically. As noed above, no model can explain he difference in price impacs if one group of rades conains more privae informaion han he oher. However, such a model exiss empirically in our case. Opion Marke Mehodology The public informaion midpoin is compued for he opions marke in wo ways. The firs mehod is a simple applicaion of he BSM formula. I combines curren sock price and pas sock and opion quoe midpoins and doesn require hisorical daa. The second mehod follows he logic of Equaion (1). I predics change in he quoe midpoin by a range of public variables including he BSM implied price from he firs mehod. The regression mehod is more sophisicaed and requires hisorical daa o esimae model parameers. The wo mehods span a large specrum of alernaive mehodologies. As he mos precise mehod should be used o esimae he execuion iming bias, we rely primarily on he regression mehod for his purpose. However, he resuls in he las secion of he paper indicae ha many invesors use a similar o he BSM approach for heir rade execuion. N BSM BSM 1 Pˆ ( K, T ) = Opion Price ( S, IV, K, T ), IV = IV i (7) N The BSM mehod consiss of wo seps oulined in Equaion (7). In he firs sep, average implied volailiy over previous 30 minues is compued 26. The pas implied volailiy provides a mapping beween opion and sock prices, similar o coefficiens in a regression. In he second sep, curren sock price 27 is ransformed ino he implied opion price wih he pas implied volailiy and he BSM formula from he firs sep 28. i= 1 26 Fifeen snapshos of implied volailiy wih wo-minue ime sep 27 Even if we use a sock price wih one second lag o allow for possible laency beween he markes, he resuls change very lile. 28 We assume no dividends and he risk free rae equal o 60-day LIBOR. Time o expiraion is measured using calendar ime. 9

11 The mehod can be viewed as a non-linear regression beween opion and sock prices. I is esimaed on he previous 30 minues and hen predics wha opion price should correspond o curren sock price. The approach is close o being model free and requires only wo main assumpions. Firs, implied volailiy changes much slower han a sock price during a rading day. Indeed, afer adjusing for marke microsrucure effecs, implied volailiy changes slowly and smoohly inraday 29. The second assumpion is ha he implied opion price is equal o he quoe midpoin on average during 30 minues before he rade ransacion 30. The second approach for compuing he public midpoin is based on a linear regression (8). P + P = α + α ( Pˆ P ) + α ( Pˆ BSM BBO + T α i i ds i i + α j j dp = ( ) = j P ) + α #ExchBid + ε 3 + α #ExchAsk 4 + (8) The change in he opion quoe midpoin over he nex hour is prediced by a baery of explanaory variables including informaion abou limi order book and shorerm price hisory. The baery accouns for he BSM model by including he BSM implied bias, he difference beween he BSM implied opion price and he quoe midpoin. The sae of he limi order book is represened by he difference beween he average quoe midpoin across all exchanges and he NBBO quoe midpoin. We also include he number of exchanges a he bes ask and bid prices. Opion and dela-adjused sock price changes are aken for 12 five-second snapshos o accommodae he mos recen price dynamics. The regression is esimaed separaely for each sock and six absolue dela (0.35 and 0.65 cu-offs) and ime-o-expiraion (60 days cu-off) bins on each day wih five second ime seps 31. The average coefficiens across all days 32 wihin each bin are hen used for predicions. 29 The populariy of he BSM model among praciioners is parially driven by is abiliy o decompose fasmoving opion prices ino he sock price componen and he slow-changing residual called implied volailiy. 30 Over long periods of ime quoed and public midpoins are equal on average. 31 As price dynamics on each day is relaively independen, his mehodology simplifies he compuaion of -saisics, and spoing he ouliers. 32 The larges and smalles coefficien values are dropped o avoid poenial ouliers. 10

12 Table 5 repors average coefficiens across all socks for en minue and one hour ime horizons which are laer used for price impac and rading cos esimaion respecively. Changes in he opion quoe midpoin are highly predicable wih R-squared of 10%. The BSM implied bias is he mos significan variable, hus he BSM model indeed capures he firs order variaion in he public midpoin. The average BBO price is he second mos significan variable. I is highly correlaed wih he implied bias bu provides some addiional informaion. Consisen wih Muravyev, e al. (2012), he opion marke lags slighly behind he underlying sock; and opion midpoin is meanrevering because of aggressive limi orders. The role of he shor-erm quoe swings diminishes as ime horizon increases. The coefficien esimaes vary lile across moneyness and ime o expiraion. Empirical analysis of he Bid-Ask Spreads and Price Impac Bid-Ask Spreads The empirical secion sars by a comparison of four bid-ask spread measures in Table The average daily quoed spread reflecs rading coss for an invesor who rades a random 34. Such an invesor will pay 8.4 cens for a round rip rade, which is 20% of an average opion price of 1.7 dollars. There are wo relaed ways o reduce rading coss: he quoed spread iming and he execuion iming. Firs, invesors can rade when he quoed spread is below average. I can be evaluaed by compuing he quoed spread a he rade imes. The spread is 6.6 cens which is a 1.8 cens improvemen over he average spreads. Invesors can also ry o achieve an improvemen over he curren NBBO price. However, here is lile NBBO price improvemen in he opions marke as he effecive spread is 6.4 cens and almos equal o he quoed spread. Indeed, more han 90% of opion rades are execued a he NBBO quoes. 33 The public bid-ask spread is wice he difference beween ransacion price and he price implied by he BSM model based on he curren sock price and he lagged implied volailiy. The effecive spread is he double difference beween rade price and quoe midpoin. The quoed spread is wice he difference beween he relevan bes quoed price and he quoe midpoin a he momen of ransacion. Finally, he average quoed spread is compued separaely for each opion from one-second snapshos on he ransacion day and hen mached o rades in a given opion. 34 End-of-he-day bid-ask spreads from OpionMerics is a special case of he average quoed spreads wih only one observaion per day. 11

13 The las and mos imporan way o improve on random execuion is he execuion iming. Invesors rely on heir own esimae of he rue price which is more precise han he quoed midpoin. They buy when he public midpoin is close o he ask price and vice versa. The public bid-ask spread is only 4.5 cens, a sunning 1.9 cen improvemen over he effecive spread. The spread is even smaller a 4.2 cens if he public midpoin is compued wih he BSM mehod. The comparison beween he four bid-ask spreads confirms ha he execuion iming is an essenial elemen of rade execuion and provides a significan improvemen over he baseline case of rading a random. Imporanly, he execuion iming affecs no only he level of rading coss bu also he relaive ranking of he underlying socks. For example, Pfizer and QLogic have he same public spreads of 4.3 cens, bu very differen quoed spreads of 7 and 9.8 cens. Unforunaely, our sample conains oo few socks o conduc a comprehensive crosssecional analysis. The execuion iming bias has increased by several imes over hree years. Figure 3 plos how he public spread decreases from 6.5 cens o 3.5 cens while he average quoed spread is unchanged a 8 cens, and he effecive spread modesly decreased from 7.5 o 6 cens. So he public spread decreases in half, while he convenional spreads change lile. The rend clearly demonsraes he real effecs of algorihmic rading on opions coss; ye i canno be deeced wih convenional measures. Our resuls for he opions marke are broadly consisen wih resuls for he sock marke documened by Hendersho, Jones, and Menkveld (2011). Indeed, here was lile algorihmic rading before he Opions Linkage conneced all opion exchanges in January which riggered a serious upgrade of exchange infrasrucure. This hisorical observaion explains he small execuion bias a he beginning of he period. As he opions algorihmic rading ook off he execuion bias seadily increased hrough Oher ime-series properies of average spreads are worh noing. Alhough rading coss for any paricular sock are quie volaile, marke average of rading coss is 35 Hendersho e al. (2011) argue ha here was lile algorihmic rading even in he sock marke pre

14 quie predicable and moves in a narrow range. In his sense, he risk of volailiy in rading coss seems o be diversifiable a leas during normal imes. The spread imeseries flucuae around a long erm rend and have a posiive auocorrelaion, bu lile volailiy clusering is observed, and he volailiy of day-o-day changes in he spreads are consan over he period. The execuion iming explains he main sylized fac abou opion bid-ask spreads, namely why dollar opion spreads increase in absolue opion dela. Figure 2 shows ha for ou-of-he-money (OTM) opions he average quoe spreads are below 7 cens, while he spread is 11 cens for ITM opions. By conras, he public spread is much flaer in dela. The spread increases from 4 o only 6 cens from OTM o ITM. For large rades, he relaionship becomes compleely fla wih 5 cen spread for ITM opions. Cho and Engle (1999) argue ha opion marke makers immediaely dela hedge afer each rade and hus pay he spread in he underlying sock. However, he heory falls shor empirically because i predics ha he difference beween OTM and ITM spreads should be less han he underlying bid-ask spread. The bid-ask spread in he sock marke is one penny, while he observed difference in spreads beween OTM and ITM opions is a leas four imes larger. Afer accouning for he execuion iming he difference becomes wo cens for rades of average size, and only one cen for large rades. These magniudes are comparable o he bid-ask spreads in he underlying sock. Thus, he execuion iming can explain why he opion bid ask spread increases in absolue dela. Finally, Table 6 provides a more rigorous condiional analysis of he iming bias measured by Equaion (5). The focus is on economic raher han saisical significance because he laer is graned by he large sample size. The iming bias is increasing in absolue dela because sock price movemens have a larger effec on ITM opions, making execuion iming easier. Average iming bias is 0.38 (or 38%), and he change from OTM (dela=25) o ITM (dela=75) will increase he bias by 0.1. Opion marke makers are aware of his effec as absolue dela becomes insignifican afer including a variable for he number of exchanges quoing bes price. The iming bias increases by 0.16 each year reflecing he increased uilizaion of algorihmic rading. As expeced, he number of exchanges quoing he bes price in he direcion of a rade is a significan deerminan of he bias. Each addiional exchange 13

15 reduces he bias by In a special case of only one exchange quoing he bes price he bias is addiionally larger by Oher explanaory variables have small economic magniude. Price Impac The execuion iming has direc implicaions for price impac. Figure 1 shows ha he observed price impac consiss of wo componens: he causal impac of rades and he expeced change in he quoe midpoin as i converges o he public midpoin. In he opions marke, he expeced quoe change is larger han he causal impac of rades. Table 4 compares observed and expeced price impacs for one, en and sixy minue horizons. The observed price impac is measured in a sandard way as a dollar change in he quoe midpoin following a rade ransacion 36. For he BSM mehod, he expeced price impac equals o he implied bias because he quoe midpoin should evenually converge o he BSM implied price. The regression mehod firs esimaes Equaion (8) on regular ime inervals separaely for each ime horizon and hen predics quoe movemens a he rade imes. Alhough en minues may no be enough ime for he public midpoin convergence, we follow he lieraure and use i as a baseline case. The observed price response o rades is rapid and large. The quoe midpoin moves by 1.13 and 1.34 cens in one and en minues respecively. Alhough, i s emping o aribue he large price impac o asymmeric informaion, in fac, he iming bias consiues mos of i. The BSM mehod predics ha even wihou a rade he quoe midpoin should move by 1.08 cens which is 81% of he observed price impac. The regression mehod predics a 0.82 cen move or 61% of he observed impac. Thus, mos of observed price impac corresponds o he expeced changes in he quoe midpoin. The public midpoin convergence is much faser afer rades han during normal ime. In he firs minue, he regression predics a 0.42 cen move, while he midpoin moves by 1.13 cens. Trade ransacions urge marke makers o updae quoes and cener hem around he public midpoin. 36 Five-minue horizon is sandard for he equiy marke, bu he opions marke is less liquid, and en minues is more appropriae. All price impacs and quoe changes are adjused for rade direcion. 14

16 Price impac is ofen sudied as a funcion of rade size o infer which rades are informed. Figure 5 his dependence wih size measured in number of conracs. There are several sylized facs o noe. The observed price impac exceeds one cen even for small rades. I is increasing for small rades and is almos fla (a wo cens) for rades of more han hiry conracs. Trades of he smalles size of one lo have larger impac han oher small rades. Bu he mos pronounced paern is ha round-size rades have significanly lower (by half a penny) price impac han non-round ones. Finally, boh he expeced price impac and he implied bias are very close o he observed price impac boh in shape and magniude. To undersand how rades change marke percepion abou he fair price, he observed price impac should be adjused by subracing he expeced quoe changes. Figure 6 plos he price impac adjused by boh he BSM implied bias and by he expeced quoe changes from he regression mehod. The regression-adjused price impac preserves basic properies of he observed price impac bu he magniudes are much smaller. The adjused price impac is below one cen for any rade size and is increasing. The round-sized rades coninue o have smaller impac bu he difference decreases from 0.5 o 0.3 cens. The BSM adjused price impac makes a big difference. I has many properies which are expeced from price impac. I sars almos from zero as rades of one conrac have impac of only 0.07 cens. The price impac monoonically increases o abou 0.6 cens. More imporanly, he difference beween round and non-round sizes disappears. Finally, Table 7 presens a condiional analysis of he observed and adjused price impacs. The quoe midpoin changes are highly predicable wih R-squared as high as 9%. The observed price impac doesn depend on opion characerisics such as absolue dela and ime o expiraion if he number of NBBO exchanges is included. As expeced, he sae of he opions limi order book is a very significan predicor of he quoe midpoin. For buy rades, each addiional exchange a he ask price reduces he observed price impac by 0.57 cens. If only one exchange is sanding a he ask price he quoe midpoin will addiionally increase by 0.56 cens. Time rend is very srong, he observed price impac increases by 0.55 cens each year. Price impac is increasing in volume, bu he slope is only 0.2 cens per hundred 15

17 conracs. Coefficien for he level of opion price is small confirming ha opion price impac should be measured in dollar raher han percenage erms. The coefficien for he expeced price response from he regression mehod is 0.78, and i becomes 0.92 in a univariae regression. The link beween observed and expeced changes is non-linear. If he expeced change is large, hen he coefficien is exacly one. Bu for expeced changes of more han 5 cens, he coefficien is only If he BSM adjused price impac is chosen as a dependen variable sriking changes are observed. Mos coefficiens become insignifican. R-squared falls o zero. Remarkably, he ime rend and he number of NBBO exchanges, which are highly significan in all oher cases, become insignifican here. These observaions ogeher wih he analysis of non-round radees in he nex secion indicae ha opion marke makers use a model similar o he BSM approach o compue he public midpoin. Trades of Non-round Size The comparison of price impacs for rades of round and non-round size provides insighs ino wha public midpoin model is used by a represenaive execuion algorihm. The non-round rades pay smaller spreads and have larger observed price impac. As discussed earlier, he simples public midpoin model, ha can explain he difference in price impacs, is he one used by a represenaive algorihm. To esimae acual rading coss, we employed he mos precise model. Conrary o his, he represenaive model doesn need o be he bes or even unbiased predicor of he fuure quoe midpoin. Round rades can be spli ino wo subgroups: one wih size divisible by en and he oher wih size ending in five. As expeced, he round lo effec is more pronounced for he round-en han round-five rades. The bes way o grasp he round lo effec is a graphical descripion in Figure 5. In he figure, average price impac is compued wihin each size caegory, hus reaing each size equally. For rades exceeding 15 los, he observed price impac is half a penny smaller for round-en han non-round rades. Remarkably, he difference has essenially he same magniude for all round-en size caegories. For he round-five rades, he difference is a quarer of a penny. Remarkably, he magniude for round-five rades is half he magniude for round-en rades in all our regressions. 16

18 The BSM model for he public midpoin can explain he round-lo effec. Indeed, Figure 6 graphically demonsraes how he difference in price impacs disappears afer subracing expeced changes in quoe midpoin from he observed price impac. For he regression model, he difference decreases o a quarer of a penny. For he BSM model, he round size effec canno be visually deeced. Thus, he BSM model, or a very similar model, is used by a represenaive algorihm. The condiional analysis in Table 7 confirms he conclusions of Figure 5 and 6. We sudy he sample of all individual rades as well as he sample of averages for each rade size as in Figures 5 and 6. The laer sample is more appropriae because i gives equal weigh o each size caegory. Indeed, here are many more 20-lo han 30-lo rades, hus 20-lo size caegory receives larger weigh in he sample of individual rades. The regression includes size and he square roo of size o conrol for global dependence beween price impac and size. Opion price is included o conrol for normalizaion of price impac which is measured as dollar difference raher han percenage of price. For he sample of individual rades, he round-en and round-five rades have 0.5 cen and 0.27 cen lower observed price impacs respecively. Adjusing he price impacs by he regression model reduces he round-lo differences in half o 0.23 and 0.11 cens. However, he BSM model explains almos all of he round lo effec, reducing he differences o 0.12 and 0.04 cens. For he sample of size caegories 37, he round-en and round-five dummies are and and are comparable o he sample of individual rades. However, for he adjused price impacs he round lo difference in price impacs becomes very small. The regression adjused price impacs differ only by 0.13 cens for round-en rades. Boh round-en and round-five differences in price impacs compleely disappear if he BSM model is used for he adjusmen. Thus, he BSM model can compleely explain he round lo effec. This resul indicaes ha he BSM model, or a very similar one, is used by a represenaive algorihm and opion marke makers. Several resuls from he previous secions poin in he same direcion. The BSM adjused price impac sars from zero and increases smoohly in size as shown by Figure 6. The number of NBBO exchanges and 37 We include only sizes of less han 100 los, because here are oo few rades for larger size caegories. 17

19 he ime rend become insignifican in he regression for he BSM adjused price impac bu are highly significan in all oher regressions in Table 7. In unabulaed resuls we find ha non-round rades are smarer mosly because a non-round amoun is placed a he bes quoes raher han because invesors wan o rade a non-round amoun. We added an ineracion beween wo dummy variables: non-round rade size and only one exchange quoing bes price in he regression of he observed impac. The coefficien for he ineracion is 0.38 cens, and he coefficien for he rounden rades decreases from o cens. Ineresingly, ou of rades larger han fifeen conracs, 60% have size divisible by en which is six imes larger compared o he uniform probabiliy case. I is hard o find a raional explanaion for why here are so many round-en rades. Conclusion. There are growing concerns ha commonly used marke microsrucure measures are inadequae in he age of elecronic rading. We show ha hese concerns are warraned. Moreover, we explain he exac mechanism which causes he problem and how convenional measures can be adjused for i. The problem arises because convenional measures rely on he quoe midpoin as an esimae of he rue securiy value. This assumpion is violaed in pracice because invesors aggregae available public informaion ino a more precise esimae. The measuremen error in he quoe midpoin manifess iself a he rade momens. Execuion algorihms ime purchases o he momens when heir public informaion midpoin is close o or above he ask price, and hus is sysemaically above he quoe midpoin. Because of he execuion iming, acual rading coss and price impac in he opions marke are abou half of wha is implied by convenional measures. No only levels are off, some securiies and ypes of rades are more exposed o he execuion iming han ohers. These differences are no capured by convenional measures. For example, rades of non-round size have larger price impac han non-round ones. The convenional explanaion would be ha non-round rades conain more privae informaion. However, he difference disappears afer adjusing for he execuion iming, which relies only on public informaion. 18

20 Therefore, he adjused measures are essenial for making inferences abou rading coss and price impac. The execuion iming provides a glimpse in he secreive world of algorihmic rading and is deep impac on modern securiies markes. 19

21 References Anand, A., P. Irvine, A. Pucke and K. Venkaaraman Persisence in Trading Cos: An Analysis of Insiuional Equiy Trades, Review of Financial Sudies, forhcoming. Amihud, Yakov, Haim Mendelson, and Lasse Heje Pedersen. Liquidiy and Asse Prices. Foundaions and Trends in Finance 4.1(2005): pp Bessembinder, H., and K. Venkaaraman. Bid-ask Spreads: Measuring Trade Execuion Coss in Financial Markes, Cho, Young-Hye, and Rober F. Engle. Modeling he Impacs of Marke Aciviy on Bid-Ask Spreads in he Opion Marke. NBER Working Paper Series No (1999). Goyenko, Ruslan Y., Craig W. Holden, and Charles A. Trzcinka. Do Liquidiy Measures Measure Liquidiy? Journal of Financial Economics 92, no. 2 (May 2009): Hasbrouck, Joel. Measuring he Informaion Conen of Sock Trades. The Journal of Finance 46, no. 1 (March 1, 1991): Hendersho, Terrence, Charles Jones, and Alber Menkveld Does Algorihmic Trading Improve Liquidiy? The Journal of Finance 66 (1) (February 1): Muravyev, D.; N. D. Pearson and J. P. Broussard Is here Price Discovery in Equiy Opions? Universiy of Illinois. Vijh, Anand M. Liquidiy of he CBOE Equiy Opions. The Journal of Finance 45, no. 4 (1990):

22 Figure 1 Examples of he execuion iming. Panel A shows a sylized example here he public informaion midpoin is consan. Invesors buy when he public midpoin is close ask and hus is above he quoe midpoin. Panel B presens a more realisic example. The public midpoin decreases bu he bid price remains unchanged for a while allowing invesors o execue heir sales. Panel C demonsraes how he observed price impac consiss of he acual impac of rades and he expeced changes in he quoe midpoin. Time and price are se on he horizonal and verical axes accordingly. Solid arrows denoe he momen and direcion of rades. Panel A. Panel B. 21

23 Panel C. 22

24 Figure 2 The public bid-ask spread is flaer in opion dela han oher spreads. The graph plos non-parameric esimaes for five ypes of he bid-ask spreads as a funcion of absolue opion dela. The spreads include he public spread (red line), he public spread for rades larger han nine los (dashed magena), quoed (blue), effecive (dashed blue), and average quoed spread (dash-do black). The public bid-ask spread is he double difference beween he ransacion price and he public midpoin. The public midpoin is based on a one hour forecas of opion price from regression (8) which includes he opion price implied from he sock marke, average quoe midpoin across all exchanges, number of exchanges quoing he bes bid and ask prices, and lagged changes in opion and sock prices. The effecive spread is he double difference beween he rade price and he quoe midpoin. The average quoed spread is compued from one day of one-second snapshos corresponding o each rade ransacion. The spreads vary beween 3 and 12 cens. The lines are esimaed wih a kernel regression based on he sample of 20 million rades for opions on 39 socks from April 2003 o Ocober Opion delas are compued from he Black-Scholes-Meron formula. 23

25 Figure 3 Execuion iming is becoming increasingly imporan over ime. The graph plos he evoluion of he public (red), he effecive (blue), and he average quoed (black) bidask spreads over he sample period. In he beginning, he spreads are comparable; however a he end, he public spread decreases in half, while oher spreads change lile. The decrease in he public spread coincides wih he algorihmic rading boom in he opions marke. The public bid-ask spread is he double difference beween he ransacion price and he public midpoin. The public midpoin is based on a one hour forecas of opion price from regression (8) which includes he opion price implied from he sock marke, average quoe midpoin across all exchanges, number of exchanges quoing he bes bid and ask prices, and lagged changes in opion and sock prices. The effecive spread is he double difference beween he rade price and he quoe midpoin. The average quoed spread is compued from one day of one-second snapshos for an opion corresponding o each rade ransacion. Each poin is an average across all opion rades on a given day. The spreads vary beween 3 and 10 cens. The sample period is April 2003 hrough Ocober

26 Figure 4 Bid-ask spreads for rades of differen size. The graph plos he public (red) and effecive (blue) bid-ask spreads as a funcion of rade size measured in los. The effecive spread is he double difference beween he rade price and he quoe midpoin. The public bid-ask spread is he double difference beween he ransacion price and he public midpoin. The public midpoin is based on a one hour forecas of opion price from regression (8) which includes he opion price implied from he sock marke, average quoe midpoin across all exchanges, number of exchanges quoing he bes bid and ask prices, and lagged changes in opion and sock prices. Noe ha large rades, non-round rades (wih size no divisible by 10), and one lo rades achieve beer han average execuion. Each daa poin is an average across all opion rades of a given rade size. The disribuion of rade size is highly skewed (roughly exponenial). Average rade size is 42, and is 50 h and 95 h perceniles are 10 and 114 conracs respecively. The effecive spread is sable around 6.5 cens. The confidence bounds are compued separaely for each rade size. 25

27 Figure 5 Observed price impac and expeced changes in he quoe midpoin. Mos of he observed response of he quoe midpoin o a rade is aribued o he convergence of he quoe midpoin o he public midpoin and no o a causal effec of he rade. Change in he quoe midpoin in 10 minues afer a rade (blue) is compared wih he BSM implied bias (black), and expeced changes in price if here were no rade (red) as a funcion of rade size. The implied bias is he difference beween he opion price implied by he BSM model from he curren sock price and he lagged implied volailiy and he opion quoe midpoin immediaely before he rade. Expeced quoe changes (red) are compued based on he coefficiens esimaed from regression (8) which includes he implied bias, average quoe midpoin across all exchanges, number of exchanges quoing he bes bid and ask prices, and lagged changes in opion and sock prices. The regression is based on regularly spaced 10-minue ime seps. Each poin is compued as a simple average across all opion rades of a given rade size. The disribuion of rade size is highly skewed (roughly exponenial). Mean rade size is 42, and is 50 h and 95 h perceniles are 10 and 114 conracs respecively. Trade size is repored in conracs each on 100 underlying shares, price impac is cens. 26

28 Figure 6 Price impac adjused for he expeced quoe changes. 10-minue quoe midpoin change is adjused for prediced changes in he opion price by subracing he BSM implied bias (blue) or by subracing a predicion from a regression model. The BSM implied bias is he difference beween he opion price implied by he BSM model from he curren sock price and he lagged implied volailiy and he opion quoe midpoin immediaely before he rade. Expeced quoe changes (in red) are compued from regression (8) of he opion midpoin 10-minue changes on he implied bias, average quoe midpoin across all exchanges, number of exchanges quoing bes bid and ask, as well as lagged changes in opion and sock quoe midpoins. The regression is based on regularly spaced 10-minue ime seps. Each daa poin is compued as a simple average across all opion rades of a given rade size. The disribuion of rade size is highly skewed (roughly exponenial). The mean rade size is 10, and is 50 h and 95 h perceniles are 42 and 114 conracs respecively. Trade size is repored in conracs each on 100 underlying shares, price impac is cens. The smoohing for he implied bias adjusmen (in black) is done via a kernel regression. 27