Agency Costs of Institutional Trading

Transcription

1 Agenc Coss of Insiional rading B Roger M. Edelen * and Gregor B. Kadlec amplin College of Bsiness Virginia ec Blacksbrg, VA [email protected] Absrac Under e pical insiional rading arrangemen a porfolio manager makes e rade decision and a rading desk execes e rade, wi execion performance evalaed agains a bencmark sc as e volme weiged average price (VWA). We develop a model wic sows a is arrangemen gives e rader an incenive o mainain a relaivel low ask qoe wen valaions rise o expedie sell rades and a relaivel ig bid qoe wen valaions fall o expedie b rades. is process inibis informaion assimilaion, casing price-adjsmen delas. We provide empirical sppor for is argmen wi several previosl ndocmened cross secional and ime series facs abo price-adjsmen delas. Jl 8, 008 * Corresponding aor. is paper was sppored in par b a researc gran from e amplin College of Bsiness. We wis o ank e following for e elpfl commens: A. Sbramanam, arn Cordia, Simon Gervais, Hsein Glen, Larr Harris, Ning Jin, Marc Lipson, Vija Singal, Bilge Yilmaz, and Seminar paricipans a Boson College, Universi of California Davis, Virginia ec, Indiana Universi, e -Grop, e Boson Researc Analss Socie, and e 007 Wesern Finance Associaion Meeings. Errors are solel e responsibili of e aors.

2 . Inrodcion A mos invesmen firms, e porfolio manager delegaes rade implemenaion o a rading desk. is division of labor beween porfolio managers and raders follows from e disinc skill ses involved wi eac ask. Experise in porfolio managemen involves, for example, analsis of acconing saemens; prodc markes; and porfolio efficienc. B conras, experise in rading involves a deailed knowledge of marke operaions; analsis of order flow, and e abili o locae conerparies for difficl-ofill posiions. is paper develops and ess a model of an agenc conflic a arises wen e porfolio manager delegaes rade implemenaion. Or model explains several ke feares of insiional rading arrangemens and provides novel predicions regarding informaion assimilaion in secri markes. As wi an principal-agen relaion, monioring of e rader s acions b e porfolio manager is an imporan consideraion. is monioring ma be informal, as in ad oc comparisons of execion prices o concrren marke prices; or formal, as in a ssemaic compaion and reporing of rade saisics vis à vis objecive (qaniaive) bencmarks. For racabili, or model analzes a common formal approac o monioring in wic e porfolio manager compares e raders execion prices o e volme weiged average price (VWA) of all rades in e marke dring e rading da. We arge a performance merics sc as is (inclding ose of a more qaliaive or informal nare) give e rader incenives a are a odds wi e objecives of e porfolio manager. Specificall, raders mainain a low ask qoe (relaive o fair vale) wen valaions rise o expedie sell rades, and a ig bid qoe (relaive o fair vale) wen valaions fall o expedie b rades. Wen e rader as

3 compleed e order e aggressive qoing beavior sops, and e sock s price sbseqenl rises (falls), reflecing e sif in valaion. raders are willing o accep less an fair vale wen selling agains rising valaions, and o pa more an fair vale wen bing agains falling valaions, becase eir performance is evalaed relaive o a pariall backward-looking bencmark (e.g. VWA). is conrarian execion sraeg locks-in posiive performance wen price-o-vwa is favorable, even if price o fair vale is nfavorable. is game of selecivel execing ose [rades] a are mos favorable is referenced in Madavan (00, page 34). In principle e porfolio manager need no gran e rader an opion o selecivel exece; se cold insead mandae immediae execion. However, doing so wold leave e rader wi few degrees of freedom o emplo is experise o minimize rading coss. s, e M faces a rade-off beween e agenc cos of graning discreion, and e agenc benefi of exploiing e rader s experise. Or model solves for e opimm level of discreion, minimizing expeced rade-implemenaion coss. e cenral predicion of or model is a is agenc conflic cases insiional raders o exece e M s order coner o sifs in valaion. Lipson and cke (006) provide direc empirical sppor for is predicion in e conex of ssemaic (marke-wide) sifs in valaion. Specificall, e sow a insiions are ne sellers wen marke valaions rise and ne bers wen marke valaions fall. Moreover, e find a e increase in insiional selling in rising markes, and bing in falling markes, is de o rade implemenaion raer an posiion decisions. is finding

4 sppors or model s conenion a e rader, raer an e porfolio manager, alers execion qani o rn coner o sifs in valaion. e conrarian nare of delegaed rade execion a arises in or model inibis e assimilaion of informaion in secri prices, casing price adjsmen delas. s, e economic imporance of e agenc conflic exends beond e isse of organizaional efficienc. Or model makes several novel predicions regarding crosssecional and ime series properies of price adjsmen delas. Or empirical analsis parallels is eoreical developmen. We firs docmen price-adjsmen delas wi respec o eqi-index fres rerns for a large sample of socks, sing a meodolog a precldes nonsncronos rading effecs. We en es e condiional predicions of e model, specificall a price-adjsmen delas are: () posiivel relaed o a sock s price-vwa raio, () negaivel relaed o lag b-sell order flow imbalances, (3) negaivel relaed o lag rading volme, and (4) posiivel relaed o e ime of da. Or findings confirm eac of ese predicions. Finall, or model predics a e degree o wic e M grans discreion o e rader, and s, e magnide of price-adjsmen delas, is relaed o e liqidi of e sock. For liqid socks wi lile opporni for price-improvemen, e M grans e rader lile discreion. For relaivel illiqid socks, were e rader s experise can lead o larger price improvemen, e M grans a relaivel ig degree of discreion. is effec arises for oer bencmarks, sc as implemenaion sorfall. e ke is a e bencmark incorporaes (formall or informall)prices a are pre-se a e ime e rader execes a rade. is gives e rader an opion wi a known srike a e ime of e rading decision. e fac a nondiscreionar algorimic rading is mos common in large-cap socks is consisen wi is predicion. See, i.e., p:// and p://advancedrading.com/goldbook006/bi_nan.jml 3

5 s, or model predics lile price adjsmen dela in large cap liqid socks b relaivel large price adjsmen delas in small cap illiqid socks. Or analsis of insiional rading as a nmber of parallels wi oer sdies of rading. Firs, e agenc conflic in or model is similar o a proposed b Harris and Sclz (998) o explain e viabili of SOES bandi rading. Second, becase e price-adjsmen delas of or model arise from demand for liqidi, or analsis is consisen wi e recogniion of ecnical raders (marke makers in or model) as providers of liqidi as opposed o exploiers of marke inefficiencies [Kavejecz and Odders-Wie (004)]. Finall, or model demonsraes anoer wa in wic marke paricipans can impede e adjsmen of prices o informaion. For example, Hasbrock and Sofianos (993) sow ow specialiss or dealers ma impede e adjsmen of prices becase of excange sabilizaion obligaions or invenor imbalances. Similarl, Admai and fleiderer (988) and Foser and Viswanaan (993) sow ow pblic limi orders and rading sraegies ma impede e adjsmen of prices. e remainder of or paper proceeds as follows. Secion develops e framework for or model of e agenc conflic ineren in delegaing rade implemenaion. Secion 3 explores e implicaions of e model. Secion 4 discsses e sample selecion, daa sorces, and meodologies sed o es e empirical predicions of or model. Secion 4 presens e empirical resls. Secion 5 smmarizes or findings. 4

6 . Model Framework and Solion. Se-p and overview ere are for economic eniies in e model represening; pblic order flow, marke makers, porfolio managers, and insiional raders. rading occrs in wo discree inervals encompassing a rading da; a morning acion and an afernoon acion. is assmpion greal simplifies e model s developmen b no generali is los in considering more freqen inervals or longer rading orizons. were Le V denoe e fair vale of e secri raded, wic follows e process M ( R ) V = V ψ, () M R is e marke rern in inerval and ψ is a pblicl observed, idiosncraic sif in vale wi prior variance (precision ). e for economic eniies in e model are described below... blic order flow e pblic order flow qani, aking e form F, as bo an informed and a noise componen, F ( E( V ψ ) ν = = ψ ν () ( V ) were is e marke price of e secri and ν is normall disribed noise rading wi variance -. blic order flow consies e onl sorce of privae informaion abo ψ : all oer eniies in e model learn abo ψ eier wen i is annonced a ime, or via raional inference from eqilibrim prices a ime -. Inelasici ( > 0) in 5

7 e informed componen of F cold be moivaed b risk aversion or adverse selecion concerns, b for ease of exposiion we ake as exogenos... Marke maker e second eni in e model is a marke maker (MM) wo onl rades agains perceived sor-orizon deviaions beween price and fair vale, wi elasici. In doing so, e MM expends effor o acqire and appl a ecnolog (e.g., ecnical analsis in Kavejecz and Odders-Wie (004)) a pariall idenifies e nare of order flow. is ecnolog ields e signal 3 U = ν η (3) were η is a random disrbance wi precision(η) =. Le S denoe e ransformaion S F ( zu ) = ψ ( zu ) = V υ (4) were z. Using S, e MM forms e condiional expecaion (appendix A) ( S, U ) = V ws E V (5) were w, and demands ( E( V... ) = ( V ws ) ( ) MM =. (6) 3 Correlaed order flow sggess a e marke rern ma also ave a noise componen, and s, e marke-maker s signal cold provide informaion abo e noise componen of e marke rern as well. In e ineres of simplici, we ignore is possibili. 6

8 ..3 orfolio manager e ird eni in e model is a porfolio manager (M) wo formlaes demands, M, based on long-orizon consideraions. lasible moives inclde fndamenal forecass of vale (forecass of, j >> ); porfolio rebalancing as in Nagle (006); Y j sareolder flow as in Edelen (999); or noise rading as in Dow and Goron (997). Becase M is based on disan (if an) forecass of Y j, e realizaion Y does no aler e M s demands. s, we ake e qani marke. M o be exogenos o e ime e exogenei of e M s demands does no mean a e M wold wan o ave e qani M filled in period nder an circmsance. For example, if e M knew a e marke price a ime was adversel inflenced b noise rading, e M mig prefer o dela e order nil e inflence of noise raders abaes. However, e M canno correcl inerpre marke condiions wio expending e ime and effor reqired o develop and implemen e MM s ecnolog. e M as limied informaion processing capaci, and is mli-asking cold ndermine performance a e primar ask of porfolio managemen. s, even og e M wold like o make M endogenos o marke condiions, as a pracical maer se canno. Insead, e M delegaes e ask of rade implemenaion o an insiional rader e for eni in e model. o e exen a e M grans discreion o e rader o reac o marke condiions, is inrodces an endogenos componen o e M s demands, even og e M s insrcions o e rader are exogenos. 7

9 ..4 Insiional rader e M emplos a rader wo is carged wi developing and implemening e MM s ecnolog o idenif noise rading and improve execion b backing awa wen ere are compeing noise raders and aggressivel filling e order agains conrar noise raders. However, nlike e MM, wo profis from is acivi, e rader as no naral incenive o expend e effor reqired o develop and implemen e MM s ecnolog, becase e rader s posiions are dicaed b e M. 4 Hence, e M ms compensae e rader in sc a wa a e rader cooses o acqire, and appl, e MM s ecnolog... rice were e marke-clearing price saisfies MM F = 0 (7) is e demands sbmied b e rader in period. Using Eq. () and (6), V M ( R ) ws ( ws ) ψ ψ υ =. (8).3. rader incenives and monioring b e porfolio manager In filling M, e M wold like e rader o reac o disorions in price cased b noise rading. Since ese price effecs are ransien, rading arond em lowers execion coss. e M canno direcl evalae sc effor, becase e M canno disingis beween e noise componen of price moves (U) and e informed componen of price moves (S). Insead, e M seeks o indce e opimal beavior b 8

10 compensaing e rader according o execion performance relaive o a bencmark. Wen a formal bencmark is emploed, e mos common meric is a volme-weiged average of ransacion prices dring e rading window, i.e., VWA. We ake is formal meric as a prox for ose cases were a less formal evalaion is condced, as i leads o a racable analsis wi explici resls..3. Compensaion framework We specif e rader s compensaion as: ( ˆ ˆ M raderwa VWA) ( ) α ( ) A φ, (9a) were: M is e arge qani specified b e M; and are e rader s execion qaniies in eac of e wo periods; A, φ and α are coice variables; and e adjsed weiged average prices for e rader and e marke, respecivel, are: ˆ ˆ raderwaˆ = (9b) VWA ˆ = ˆ ˆ ; (9c) ˆ and ˆ are e marke clearing prices in e morning and afernoon acion, respecivel, possibl adjsed for facors observable o e M. 5 Absen adjsmens o price, is performance is e sandard VWA meric wi a penal for non-execion. 6 4 Wo owns e rade if i is dicaed b bo e M and e rader? How are e profis spli? If e are pooled, en e link beween e rader compensaion and effor is loosel speaking wice as nois as wi direc compensaion. Likewise e M s incenives are weakened. 5 For example, e M cold adjs prices for marke rerns dring e period o alleviae some of e saleness in e bencmark. e derivaion incorporaes ese poenial price adjsmens. However, o simplif or discssion of e model s ke elemens we defer is refinemen o appendix G. 6 In pracice, VWA is picall applied on a dail basis (see i.e., p://en.wikipedia.org/wiki/vwa), so we ink of e wo periods in e model as one rading da, wi a morning and an afernoon acion. e execion bencmark is e average clearing price in ose wo periods. 9

11 e firs erm in Eq. (9a), A, is a fixed pamen o cover e rader s paricipaion cos; e second erm is e rader s compensaion for execion performance relaive o VWA; and e ird erm is a penal for parial execion. We make e simplifing assmpion a marke volme is eqal in e wo periods. e parameer φ is e fracion of price-improvemen gains passed on o e rader as compensaion. e parameer α is e penal e M imposes for incomplee execion. e M can indce fll execion b coosing α/φ o be large. However, is inibis e rader s effors o lower execion coss. 7 e compensaion sceme grans e rader an opion o pariall fill e order in adverse marke condiions, and o asmmericall exece e order in volaile marke condiions (i.e., more an alf in one period, less an alf in e oer). is discreion lowers execion coss as e rader explois e MM s ecnolog o idenif ransien deviaions beween price and fair vale cased b noise raders, b i also inrodces an agenc cos. In pariclar, e rader can alwas claim a difficl marke and pariall fill e order wen marke prices fade awa from e order for reasons nrelaed o noise rading. For example, pariall filling a b order in a rising marke cases raderwa ˆ o il oward e lower, firs period price. s, iger compensaion is awarded. Likewise, pariall filling a b order wen e sock experiences a posiive idiosncraic signal, S cases raderwa ˆ o il oward a lower price. e explici penal (α > 0), serves o conerac is agenc cos. 7 M is qadraic penal fncion raer an a consrained linear penal ( ), makes e calcls far more racable, as we don ave o do e bondar cecks and rncaed expecaions a arise wi e linear seing, see Appendix A.3. Moreover, i is consisen wi e expeced opporni cos of sbmiing a nex-da marke order. 0

12 and One final observaion regarding e compensaion framework: e rader cooses o maximize: max, ( ˆ M ) ( ) α( ) ˆ ˆ E A φ ˆ (0) wic is eqivalen o min, φ E ˆ α M ( ). () s, prices onl ener e analsis b wa of e rern from period o, ˆ..3. Adjsmens o price Wrie e sock rern in period as FV N ˆ ε. () FV M ψ, were = V R ( ws) ws N = zu, ε = 3 υ (( ψ ws ) ( zu )). (3) Eqs. (3) arises from e rader s se of e MM s ecnolog o decompose e sock FV price ino: a componen ( ) de o fair-vale canges a impac e rader s N compensaion; a componen ( ) de o noise raders; and a componen ( ) rader canno idenif as eier informed ( ψ ) or noise ( υ ) 3 ws zu ε a e. We will

13 laer see a agenc coss of insiional rading are aribable o e of rerns. FV componen Demands e rader cooses demands o minimize Eq. () sing Eq. (3): and recrsivel. Firs e rader cooses min, φ E ˆ α M ( ). (4) Solving e firs order condiion w.r.. ields φ, FV N M ( ) α ( ) 0 =, (5) FV N ( ) M ( Ω)( ) = Ω (6) were we ave sed φ Ω = for noaional convenience. Ω indicaes e relaive φ 4α empasis a e M places on rading profis, φ, verss iing e arge qani, α. Nex, e rader cooses period demands, incorporaing Eq. (6), ielding: 8 = M N. (7) M / reflecs e defal period qani. Eq. (7) indicaes a e rader cooses o deviae from a qani. Finall, rerning o e afernoon acion, Eqs. (6) and (7) ield: 8 Calclaions in Appendix B.

14 N FV ( ) N M Ω = M Ω N FV ( ) ( ) =. (8a). (8b) were e firs brackeed expression reflecs e period defal qani e M s arge demands less a filled in period and e second brackeed erm reflecs e rader-imposed qani adjsmen in period. 3. Model Analsis is secion examines e iniion beind e demand expressions of secion, and presens several predicions a arise from e model. 3.. Inerpreing e demand eqaions In bo period and period, e rader deviaes from e demands sog b e porfolio manager, M /. In period, is deviaion reflecs e rader alering demands o coner is signal of noise rading, N. In period is deviaion reflecs bo e signal of noise rading, N, and fair-vale price canges no acconed for in e rader s performance evalaion, FV. rading coner o a signal of noise is precisel e aim of e M, as discssed in secion..4: dela rading in periods wi emporaril ig rading coss, accelerae rading in periods wi emporaril low rading coss. Since e speclaion orizon falls wiin e wo-period rading window a e M gives e 3

15 rader, is speclaive deviaion from M / is recified wio an impac on e overall qani raded,.9 e appearance of FV (i.e., fair-vale canges in price a are orogonal o e rader s informaion) in period- demands reflecs e agenc cos of delegaing rade implemenaion. From e M s perspecive, fair-vale canges in price sold ave no bearing on e qani raded becase M is exogenos and assmed o be independen of e ig-freqenc informaion conained in rader maniplaes order qani in response o FV FV. Nevereless, e, bing less (or selling more) in period wen 0 and bing more (or selling less) wen 0. Doing so FV > FV < mimics e beavior a e M wans o see in response o ransien price disorions cased b noise raders, and e M canno idenif e re sorce of e price move. Noe a fair-vale canges in price dring period a are orogonal o e FV rader s informaion ( ) do no inflence period demands. ese canges affec e period price as mc as e period price in expecaion, ence bo E [ raderwaˆ ] and E [ VWAˆ ] sif p or down b FV and e rader as no reason o skew rading owards, or awa from, period. B conras, canges in fair vale price in period do no affec e price of rades alread execed in period, so skewing rading owards, or awa from, period in response o FV is in e rader s ineres. 9 e special case of φ = 0 sold be singled o, becase e rader en as no incenive o reac o noise rader disorions in period wen φ = 0; is onl concern is complee execion. s, e cooses = M b oerwise period demands are indeerminae. We erefore assme eqal proraion across periods in is special case. 4

16 Anoer difference beween period and demands is e Ω coefficien in period demands. Recall a Ω (Eq. 6) indicaes e relaive empasis a e M places on rading profis verss complee execion of arge demands ( M ). Becase discreionar rading b e rader in period (i.e., deviaion from M /) can be reversed in period, e rader fll prses opporniies o improve execion performance in period (if e receives some benefi for doing so, i.e., φ > 0). B conras, in period, e rader is pnised for deviaing from e arge order qani if Ω < becase e rader as no cance o recif e difference. 3.. Resls on rader beavior ese demands sgges an explanaion for e findings in Lipson and cke (006), wic sows a insiions are ne sellers wen markes are rising and ne bers wen markes are falling. In pariclar, M R is a ke ingredien o FV. According o Eq. (8), e rader will b less (sell more) wen M R > 0 becase e M does no disingis is seing from one in wic noise rader bing (selling) impars a ransien increase b (sell) execion coss. a is, e volme of orders sbmied b e rader o e marke is negaivel relaed o M. Or model is also consisen wi a second resl in Lipson and cke: e increase in insiional selling in rising markes, and bing in falling markes, can be aribed enirel o rade implemenaion (i.e. e discreion of e rader) raer an posiion decisions (e discreion of e M). Noe a in or model, e M reqess a fill of We smmarize is resl as R M irrespecive of marke condiions. 5

17 roposiion e volme of execed insiional b (sell) orders is negaivel (posiivel) relaed o marke rerns, even if e porfolio manager s order volme is independen of e marke. According o Eq. (8), marke rerns are no e onl facor giving rise o an opporni o exploi e compensaion sceme. 0 e rader can also exploi idiosncraic rerns de o pblic informaion, i.e., ( ψ ) ws ; and privae informaion, ws. In bo cases, e M doesn know a ese price moves are no driven b noise rading. We smmarize is resl as roposiion e volme of execed insiional b (sell) orders is negaivel (posiivel) relaed o permanen, idiosncraic sock rerns a can be aribed o bo pblic and privae informaion. Again, is effec occrs a e rading level, raer an e porfolio managemen level. roposiion wo is no examined in Lipson and cke. Or final proposiion regarding rader beavior is an exisence resl. Appendix C sows a e rader s expeced compensaion, C Comp ( Ω σ ( Ω) σ ) φ = A FV N (9) 4 were C Comp denoes e M s expeced compensaion cos. Since A is e rader s compensaion nder e no-effor sraeg of compleel filling e order a VWA, and all erms in Eq. (9) are posiive, is esablises 0 In Appendix G we consider an adjsed VWA meric a immnizes agains exploiaion indced b marke rerns. 6

18 roposiion 3 e rader cooses o emplo e MM s ecnolog and appl discreion in execing e order, raer an following VWA exacl, if e M assigns some weig o price-improvemen in e compensaion Eq. (4) (i.e., φ > 0) and eier ere is some price flcaion de o noise rading a e rader can idenif and sccessfll exploi (i.e., σ N > 0), or ere is an exogenos componen o e sock s rern (driven b e marke or idiosncraic pblic informaion, i.e. σ FV > 0). e firs blle represens e essence of e M s objecive in emploing e compensaion sceme. e second blle represens an agenc cos. B assmpion, e M does no ave sfficien ecnolog, ime, or experience o discriminae beween e wo moives, so e M s performance is affeced b bo facors. Given bo a benefi and a cos o e compensaion arrangemen, i is no obvios a e M will in fac coose o ire and gran discreion o e rader in e firs place. e M cold exece according o VWA sing marke orders, or insis a e rader compleel fill e order. However, in bo cases e rader is lef wi no degrees of freedom o lower execion coss. e M ires e rader and emplos e compensaion sceme if e expeced benefi (beer execion) exceeds e agenc cos of exploiing e arrangemen. is is analzed in e nex secion e porfolio manager s decision We define e oal expeced coss associaed wi e M s order as e sm of wo componens. e firs componen is e relaive execion cos of compleel filling e order (comparing acal o a poeical VWA sraeg), and e second is e rader s compensaion. 7

19 We evalae relaive execion coss b inrodcing a ird period, in wic e M M execes e qani ( ) wi a marke order. We en add e cas flow from is execion o e cas flow from e rader s execions o ge oal cas flow. Finall, we compare is cas flow o a wic wold ave obained ad e M M sbmied a marke order for / in eac of e firs wo periods. Appendix D sows a is relaive cos of compleing e order, sing e rader verss e poeical VWA sraeg, can be expressed as Exec C = E0 3 M ( VWA) ( ) (0) were C Exec denoes e relaive cos of execion. A negaive vale for C Exec indicaes a e rader improves execion performance. e rader will be ired if is benefi exceeds e cos of compensaing e rader, C Comp (from Eq., 9) i.e., if e ne cos of iring e rader is negaive. Appendix E sows a e ne cos of iring e rader eqals ( 3Ω 5Ω ) 5 σ N A Ω σ FV, () 4 4 and a e M s opimal coice for Ω, minimizing Eq. (), is Ω * = 3 0 N ( σ σ ) FV σ N <. () Eq. () sows a wen σ FV (volaili of price cange e rader knows o be permanen) is ig, Ω * is small and e M ps less weig on rading profis in Eq. (0) and more weig on fll execion. Conversel, a larger predicable noise-rader componen makes graning 8

20 discreion o e rader profiable, and e M cooses a iger Ω *. Appendix E also esablises roposiion 4 e M is beer off iring a rader, raer an rading algorimicall (i.e., M sbmiing a marke order for / eac period), if and onl if e rader s fixed cos, A, saisfies σ N 3 A * < Ω. (7) 4 However, if e M does emplo a rader, en e M will gran e rader discreion o pariall fill orders. e firs par of proposiion 4 is a cenral resl of e paper, i esablises a e M will presen e rader wi a gameable compensaion arrangemen. A gameable compensaion sceme is a necessar conseqence of e asmmeric skill, experience, and informaion ses of e rader verss e M. Becase e M canno conrac direcl on effor, e acceps e second-bes conrac agenc coss nowisanding becase i improves is welfare. Implemenaion sorfall, mandaor execion, and oer alernaives I is ineresing o conras e VWA bencmark wi an alernaive bencmark, implemenaion sorfall proposed b erold (988). Implemenaion sorfall (IS) is based on e difference beween e execion price and e decision price (price a e ime e M s order was sbmied). Recall a, nder VWA, e rader explois e fac a in period 50% of is performance bencmark as been se prior o e ime e cooses. B conras, nder IS 00% of e bencmark is se prior o e ime e rader cooses bo and. Hence, bo e incenive and e opporni o 9

21 maniplae performance are greaer nder IS. Moreover, IS is sbsaniall noisier becase all rerns dring e rading window appear in e rader s compensaion. is implies a e cosen Ω is lower, and e gains from MM ecnolog are lower. A ke elemen beind e poenial gaming of ese bencmarks is e fac a e rader as an opion o pariall fill e order. Some ave arged a e solion is o force execion a e nex da marke price if e order goes nfilled, and calk i p o e rader s compensaion. If ransien noise rader deviaions persis, is will moivae e rader o ignore em, and js rade VWA, wic we know is sbopimal. If e don persis, is is eqivalen o forcing fll execion in e las period wic we ave sown is sbopimal..8. rice adjsmen delas Le s inrodce a ird period, sbseqen o e afernoon rond of rading, were e price of e sock is forced o is fair vale. Noe a, is is no a rading period i is js a ool o incorporae erminal expeced vale and is eqivalen o appling an expecaion o e vale afer e second rond of rading. s e rern from period o period 3 represens e average rern sbseqen o rading. roposiions 5 and 6 smmarize e model resls on price adjsmen delas: roposiion 5 e period rern on e sock (from iniial vale, 0, o is period vale, ) reflecs a bea of agains e concrren marke rern (eqal o is re bea). Moreover, ere is no covariance beween e period rern of e sock and e period rern of e marke. s, ere are no price adjsmen delas arising in e morning (period ) acion. Implemenaion sorfall does address some gameable aspecs of VWA. However, or ineres is in e similari, raer an differences, beween VWA and IS 0

22 roposiion 6 e rern of e sock from period o period reflecs a bea of agains e concrren marke rern, wi φ * as in Eq. (). e period 3 rern of e sock (from is period vale o is period 3 (fair) vale) posiivel covaries wi * φ e period marke rern, wi a lag-bea coefficien of. s, wile e price evenall fll reflecs is period fair vale, i does so onl wi a dela. * φ ese resls follow from e demand eqaions, (5) and (6), and e price Eqs. (8) and (9). e deails are given in Appendix F. ere are no price-adjsmen delas in e morning acion (roposiion 4) becase e rader does no a a ime ave an informaion abo is expeced execion price verss VWA. B conras, in e afernoon acion, e rader knows weer e execion price (and rogl alf of raderwa) will be iger or lower an VWA. s, e rader can maniplae raderwa (raise for a sell, lower for a b) b adjsing e execion qani in e afernoon acion. For example, wi a sell in a rising marke, overloading e afernoon acion ps more weig in raderwa on e (iger) afernoon price, casing raderwa o exceed VWA. Likewise, wi a sell in a falling marke, nderloading e afernoon acion ils raderwa owards e iger morning acion price, casing raderwa o exceed VWA. An imporan corollar o or resls on price adjsmen delas relaes o cross secional variaion. In pariclar, being a fncion of φ *, e severi of price adjsmen delas in or model depend on S. Socks wi ver deep markes, and lile price disorion from noise raders (e.g., large cap, eavil raded socks) are no likel o exibi maerial price adjsmen delas according o or eor. Moreover, Ms are no

23 likel o give raders mc discreion o maniplae execion relaive o VWA for ese socks. s, or model also ields e following Corollar e price adjsmen dela converges o 0 as 0. s, insiions do no indce maerial price-adjsmen delas in e mos liqid secriies. Moreover, e M ends o se low-cos, mecanical VWA sraegies for ese secriies. 3. Empirical Analsis e cenral predicion of or model is a an agenc conflic cases insiional raders o exece rades coner o sifs in valaion, casing price-adjsmen delas. As developed in e Appendix, is predicion applies o bo ssemaic and idiosncraic sifs in valaion. However, or ess focs on ssemaic sifs in valaion as i provides a more readil idenifiable empirical specificaion. Specificall, we regress marke-adjsed sock rerns following large ssemaic informaion evens (eqi index fres rerns) on prox variables for agenc conflic as prediced b or model: price-vwa raio, b-sell order flow imbalance, rading volme, and ime of da. is secion describes or sample selecion, daa sorces, and e meodolog sed o condc or ess. 3. Sample Or sample is drawn from e niverse of all U.S. domiciled common socks raded on e New York Sock Excange, American Sock Excange, or Nasdaq dring e period Janar 00 rog December rogl 7000 socks. Becase of e immense daa reqiremens of or ess, we resric or sample o socks were or poeses regarding price-adjsmen delas (ADs) are mos relevan.

24 e firs limiaion imposed on e sample relaes o a sock s marke bea. Becase or prox for informaion evens is e rern on eqi index fres, e poenial for a sock s AD is direcl relaed o is bea (see Calmers, Edelen, and Kadlec (00)). s, we exclde socks wose monl bea esimae is less an is screen eliminaes 43% of e niverse: % de o insfficien daa o esimae bea (36 monl rerns), and % de o an esimaed bea less an 0.5. e second limiaion on e sample relaes o e pical oldings of insiional invesors. Several sdies docmen a insiions old few micro-capializaion socks [Falkensein (996)]. s, we exclde sock s wose oal marke capializaion is less an $00 million (e lower bond for addiions o e S& 600 small cap index is $300 million). is screen eliminaes 50% of e ig-bea niverse. Or final sample consiss of 00 socks. anel A of able presens smmar saisics of varios caracerisics of or sample socks. e average (median) sample sock as a marke capializaion of $5. billion ($0.7 billion), sare price of $57 ($), monl bea of 0.85 (0.8), average dail rern of (0.0007) and sandard deviaion of dail rern of (0.03). e proporion of sample socks lised on e New York Sock Excange, American Sock Excange, and Nasdaq are 53 percen, 3 percen, and 44 percen, respecivel. ose socks removed de o marke capializaion ave an average bea of.35, s e average bea of e remaining sample rns o o be less an despie rncaing a

25 3. Daa 3.. Fres ransacion daa rice adjsmen delas ms be assessed wi respec o some informaion se. Or prox for informaion is e rern on e mos relevan index fres conrac for eac sock. More specificall, we esimae single-facor marke model for eac sock sing monl rerns on e S& 500, Nasdaq 00, and Rssell 000 indices, and coose e index wi e iges R. We en se inra-da prices on e mos acive index fres conrac on e Cicago Mercanile Excange for e cosen index. e dae comes from ick Daa, Inc. Becase ese conracs rade a porfolio of asses via a single secri, ere is lile reason o expec sprios predicabili from nonsncronos rading in is informaion sorce [see i.e., Bodok, Ricardson, and Wielaw (00)]. e serial correlaion of dail rerns for e S& 500, Nasdaq 00, and Rssell 000 fres conracs dring 00 are 0.04, 0.03, and 0.0, respecivel. 3.. Sock ransacion & qoe daa We collec ransacion prices, volme, and bid and ask qoaions for or sample socks from e NYSE s A daabase. Following Hasbrock (003) we se onl rades and qoes from e primar excange for eac sock. e A daabase idenifies apical rades and qoes. We exclde all rades a are baced; execed as par of a baske rade; or repored o of seqence.. We also exclde qoes a are idenified as eier non BBO eligible (bes effors basis), or immediael following a rading al. We appl filers o remove observaions a ma be sbjec o daa enr errors (ransposed and dropped digis). We eliminae ransacions and qoes wi reversals of 4

26 greaer an 0 percen over a seqence of ree observaions. Following Keim (989), we eliminae qoes were e bid-ask spread is greaer an 0 percen of e price for socks priced over $0 dollars or greaer an $ for socks priced nder $0 dollars. Finall, we eliminae all ransacions a occr following a qoe a was eliminaed. o obain a more accrae emporal ordering of rades and qoes, we adjs e ime samp for rades o correc for reporing delas in rades relaive o qoes as docmened in Lee and Read (99). However, we se a second adjsmen as opposed o a 5 second adjsmen de o e fac a e reporing dela is sbsaniall smaller in or more recen sample period. anel B of able presens smmar saisics of varios rading caracerisics for e sample socks. e average (median) sample sock as a relaive qoed bid-ask spread of (0.0047), a relaive effecive bid-ask spread of (0.008), rades 437 (07) imes per da wi dail volme of. (0.) million sares. 3.3 Meodolog 3.3. Measremen Isses Varios sdies calibrae e imporance of nonsncronos rading wi e general conclsion a rogl alf of e serial correlaion of observed dail porfolio rerns can be aribed o asncronos ime samping of ransacions [Kadlec and aerson (999)]. 3 Becase or focs is real price-adjsmen delas, i is imperaive a we emplo a meodolog a is free from nonsncronos rading effecs. A common means for correcing for nonsncronos rading is o se e midpoin of e bid and ask qoe in place of ransacion prices. However, evidence sggess a bid and 3 For sdies of nonsncronos rading and serial correlaion see i.e., Fiser (966), Lo and MacKinla (990), Bodok, Ricardson, Wielaw (994), and Bodok, Ricardson, Wielaw (00). 5

27 ask qoes are eqall sale in e absence of a ransacion [Calmers, Edelen, and Kadlec (00)]. o ensre proper emporal ordering of or dependen and independen variables, we measre e dependen variable (nex-da rerns of socks) following a rade and e independen variables (index fres rerns, price-vwa raio, b-sell order imbalance, volme) prior o a rade. Specificall, we define an informaion even as an economicall meaningfl rern (larger an 60 basis poins in magnide) on e sock s relevan index fres conrac over e preceding nine mines. Afer idenifing an informaion even, we look for a rade in e sock dring e inerval 60-0 seconds afer e even. If an iniiaing rade ook place dring is window, we ave a valid observaion -- a is, we can confirm a or variables ave e proper emporal ordering. We en calclae e sock s sbseqen one-da rern sing e bid-ask midpoin prior o e iniiaing rade, and e bid-ask midpoin a marke close on e following rading da. ese sbseqen one-da rerns are en adjsed for marke moves sing e sock s monl bea imes e rern on e relevan fres conrac over e exac same ime inerval. Eac of e explanaor variables sed in e analsis is measred over e same nine mine window sed o idenif informaion evens. o redce compaional reqiremens we smmarize qoes and rades on a mine-b-mine basis, keeping onl e las observed qoe and rade for a given sock dring a given mine of e rading da. s, wen we refer o a rade or qoe, we are referring o e las rade or qoe of a mine. 6

28 3.3. Regression Specificaions o es or model s predicions regarding insiional rading and priceadjsmen delas we esimae e following pooled cross-secional and ime-series regression: ADJR MSM e j j = a b Index j b b3 BSell j b4 rading j b5 VWAj (34) were: ADJR is e sbseqen one-da rern, adjsed for e concrren marke rern Index is e sock s relevan eqi index fres rern. AS 90 MINS??? /VWA is e sock s crren midpoin price divided b is crren VWA for e da. BSell is e lag b-sell order flow imbalance. We emplo ree alernaive specificaions for is measre: signed volme, signed sare rnover, and signed nmber of rades. rading is e nsigned lag rading acivi measred ree alernaive was: sare volme, sare rnover, and nmber of rades. MSM is e ime of e even measred in mines since midnig. We esimae separae regressions for negaive and posiive informaion evens (index fres rerns) o allow for differences in e dnamics of price-adjsmen delas following negaive vs posiive informaion. 4 able repors smmar saisics for e variables sed in e above regressions. Colmn repors vales for negaive informaion evens (index < ), wile colmn j j 4 One mig expec differences in price-adjsmen delas de o facors sc as sor sale consrains. 7

29 3 repors vales for posiive informaion evens (index > ). For prposes of comparison, colmn repors vales for non-informaion evens (abs(index) < 0.000)). A nmber of resls are noewor. Firs, price-adjsmen delas following negaive informaion evens are greaer in magnide an price-adjsmen delas following posiive informaion evens. For example, e average ADJR following a negaive informaion even is 36 bp below e average non-informaion ADJR. B conras, e average ADJR following a posiive informaion even is 4 bp above e average noninformaion ADJR. Second, e order flow imbalance dring negaive informaion evens is smaller an e order flow imbalance dring posiive informaion evens. is is o be expeced (bs oweig sells dring a rising marke, and vice versa). Finall, rading acivi is considerabl iger for bo negaive and posiive evens an for non informaion evens. 3.4 Regression Resls able 3 repors coefficien esimaes and -saisics (in pareneses) for e varios regression specificaions. anel A repors esimaes for regressions of negaive informaion evens wile panel B repors esimaes for regressions of posiive informaion evens. e colmns of able 3 correspond o differen specificaions of b-sell order flow imbalance and rading acivi. e coefficien esimaes of able 3 are consisen wi e predicions of or model. Firs, price-adjsmen delas are posiivel relaed o e rice-vwa raio. s, nex- 8

30 da sock rerns are more negaive following negaive marke rerns wen rice-vwa is low. is is consisen wi raders incenive o rade aggressivel (passivel) on e b (sell) side wen rice-vwa is low. Likewise, sock rerns are more posiive following posiive marke rerns wen e rice-vwa is ig, again consisen wi e model. For example, from colmn of panels A and B, e coefficiens for rice- VWA are ( = 6.40) and ( = 5.84) for e negaive and posiive informaion even regressions, respecivel. Wilesome of or model s predicions are consisen wi oer explanaions of price-adjsmen delas, is predicion appears o be is niqe o or model. Second, price-adjsmen delas are negaivel relaed o lag b-sell order flow imbalance. From colmn of panels A and B, e coefficiens for b-sell volme imbalance are ( = -.07) and ( = -6.36) for e negaive and posiive even regressions, respecivel. 5 ird, price-adjsmen delas are negaivel relaed o freqenc of rade. From colmn of panels A and B, e coefficien on volme is posiive in e negaive marke rern regression, ( =3.), and negaive in e posiive marke rern regression, ( = -4.40). Finall, price-adjsmen delas are posiivel relaed o e ime of da. From colmn of panels A and B, e coefficien on MSM is negaive and significan, ( =-3.33), in e negaive marke rern regression and posiive and significan, 0.0 ( =.0), in e posiive marke rern regression. As wi rice-vwa, is relaion appears o be niqe o or explanaion of price-adjsmen delas. Noe a inferences 5 is relaion beween rerns and lag b-sell order flow imbalance is also consisen wi price reversals de o price pressres cased b order imbalances [Cordia, Roll, and Sbramanam (00), and Cordia and Sbramanam (004)]. We laer provide evidence wic aemps o isolae ese wo effecs. 9

31 from specificaions sing alernaive measres of b-sell order flow imbalance and freqenc of rade (colmns and 3) are nearl idenical o ose discssed above. A naral concern is a or proxies are capring oer forms of predicabili in rerns as opposed o price-adjsmen delas. For example, i is possible a rice- VWA is capring some aspec of momenm og momenm is picall defined wi respec o mc longer inervals. Similarl, Cordia and Roll, and Sbramanam (004) also docmen a negaive relaion beween sock rerns and lag order flow imbalance wic e aribe o price-pressre reversals. o pariall address is concern we esimae e same regression specificaions sing non-informaion evens. a is, observaions were e lag marke rern is close o zero. If e prox variables are picking p predicabili a is nrelaed o lag marke rerns, e sold be invarian o sc pariioning -- wi one excepion. Or model predics a posiive relaion beween nex-da rerns and rice VWA regardless of e marke rern, and s, e regressions are no able o discriminae beween or model and oer poenial poeses regarding is variable. We can, owever, sed some lig on e oer variables. anel C of able 3 repors coefficien esimaes (-saisics) for regressions sing non-informaion evens (abs(lag index rern) < 0.000). As expeced, e coefficien for rice-vwa is posiive and significan in all regressions. However, e coefficien for b-sell order imbalance is negaive and significan for all regressions inclding e one were ere is no discernable informaion even. s, some of e proxies appear o capre oer forms of microsrcre relaed predicabili. However, e isse is no weer e proxies capre oer forms of predicabili b raer weer e 30

32 specificaion of or model sarpens e predicive power of ese variables in a manner a is consisen wi or model. o a end e answer appears o be es. In pariclar, e coefficiens of mos of or proxies are larger in magnide (in e proper direcion) and significance in e regressions sing informaion evens an in e regression sing non-informaion evens. 4. Smmar and Conclsions is paper develops and ess a model of an agenc conflic a arises wen porfolio managers delegae e ask of rade implemenaion. e cenral resl of or model is a raders aggressivel fill sell orders in rising markes and b orders in a falling marke. Likewise, e end o leave nfilled b orders in rising markes and sell orders in falling markes. A corollar o is resl is a widespread se of delegaed rading cases price-adjsmen delas. Or model ields a nmber of esable implicaions regarding cross-secional and ime-series properies of price-adjsmen delas. Using ransacions daa, we docmen several condiional caracerisics of price-adjsmen delas a are consisen wi or model. Specificall we find a price-adjsmen delas are: () posiivel relaed o socks price-vwa raio, () negaivel relaed o lag b-sell order flow imbalance, (3) negaivel relaed o lag rading volme, and (4) posiivel relaed o ime of da. However, e mos compelling evidence for or model comes from e wo principal findings in Lipson and cke (006). e sow a insiions are ne sellers wen markes are rising and ne bers wen markes are falling, and a is paern is de o rade implemenaion raer an posiion decisions. 3

33 Or model of price-adjsmen delas as a nmber of parallels wi prior sdies of rading. Firs, e agenc conflic of or model is similar o a proposed b Harris and Sclz (998) o explain e viabili of SOES bandi rading. Second, becase e price-adjsmen delas of or model arise from demand for liqidi, or analsis is consisen wi e recogniion of ecnical raders (sor-erm raders in or model) as providers of liqidi as opposed o exploiers of marke inefficiencies [Kavejecz and Odders-Wie (004)]. ird, or model demonsraes anoer wa in wic marke paricipans impede e adjsmen of prices o marke informaion. For example, Hasbrock and Sofianos (993) sow ow specialiss or dealers ma impede e adjsmen of prices becase of excange sabilizaion obligaions or invenor imbalances. Similarl, Admai and fleiderer (988), Foser and Viswanaan (99) sow ow pblic limi orders and rading sraegies ma impede e adjsmen of prices. 3

34 Figre Binomial model of rading da rerade Morning Acion Afernoon Acion Node 3 Exece = U Sbmi condiional demands {U 3, D 3 } o afernoon marke Exece = U 3 Exece = D 3 Node Sbmi condiional demands {U, D } o morning marke Node Exece = D Sbmi condiional demands {U, D } o afernoon marke Exece = U Exece = D as are deermined b: N S = S N S = S

35 able Descripive Saisics for Sample Socks able repors descripive saisics for 00 sample socks drawn from e niverse of 7000 U.S. domiciled common socks lised on e American Sock Excange, New York Sock Excange, or Nasdaq dring e period Janar 00 rog December 00. e final sample (00) excldes socks wi esimaed beas less an 0.50 and marke capializaion less an $00 million. anel A: Size, Risk, and Rern Caracerisics Mean Median 0 ile 90 ile Marke Cap (Millions) Sock rice Bea Average Dail Rern Sandard Deviaion anel B: rading Caracerisics Mean Median 0 ile 90 ile Dail Volme (osands) Dail rades oed Spread Effecive Spread

36 able Descripive saisics of AD regression variables able repors mean (median) vales for variables sed in price-adjsmen dela (AD) regressions. e dependen variable, ADJR, is e nex-da marke adjsed rern for e sock following an informaion even. We define ree pes of informaion evens based on e rern of a relevan index fres over e preceding 90 mine period: negaive informaion (Index< ), non informaion (abs(index)<0.000) and posiive informaion (Index>0.0060). All independen variables are measred over e same 90-mine inerval. rice-vwa is e raio of e midpoin of e crren bid-ask qoe divided b e volme-weiged average price. BSell () is a measre of order flow imbalance based on e difference beween b and sell volme, b and sell rnover, or b and sell rades. rading () is a measre of rading acivi based on volme, rnover, or nmber of rades. MSM is e nmber of mines since midnig. Negaive Neral osiive ADJR (-.006) (0.004) (0.007) Index (-.008) (0.0000) (0.008) rice-vwa (0.996) (.000) (.004) BSell (volme) (-00) (000) (700) BSell (rnover) (-0.040) (0.0) (0.060) BSell (rades) (-) () (7) rading (volme) (5) (38) (5) rading (rnover) (0.0008) (0.0005) (0.0009) rading (rades) (69) (54) (7) MSM (835) (799) (87) Observaions

37 able 3 Regressions of nex-da sock rerns on lagged rading caracerisics Coefficien esimaes (-saisics) from pooled cross-secional and ime series regressions of marke-adjsed nex-da sock rerns on lagged index fres rerns and rading caracerisics. e dependen variable, ADJR, is e nex-da marke adjsed rern for e sock following a informaion even. We define ree pes of informaion evens based on e rern of a relevan index fres over e preceding 90 mine period: negaive informaion (Index< ), non informaion (abs(index)<0.000) and posiive informaion (Index>0.0060). All independen variables are measred over e same 90-mine inerval. rice-vwa is e raio of e midpoin of e crren bid-ask qoe divided b e volme-weiged average price. BSell () is a measre of order flow imbalance based on e difference beween b and sell volme, b and sell rnover, or b and sell rades. rading () is a measre of rading acivi based on volme, rnover, or nmber of rades. MSM is e nmber of mines since midnig. anel A: Negaive Informaion Regressions Model 3 Index (0.78) (.6) (0.96) rice-vwa (6.40) (6.35) (6.76) BSell (volme) (-.07) BSell (rnover) (-.77) BSell (rades) (-.08) rading (volme) (3.) rading (rnover) (5.8) rading (rades) 0.00 (3.74) MSM (-3.33) (-.7) (-3.36) Adj. R-sqare

38 able 3 Regressions of nex-da sock rerns on lagged rading caracerisics Coefficien esimaes (-saisics) from pooled cross-secional and ime series regressions of marke-adjsed nex-da sock rerns on lagged index fres rerns and rading caracerisics. e dependen variable, ADJR, is e nex-da marke adjsed rern for e sock following a informaion even. We define ree pes of informaion evens based on e rern of a relevan index fres over e preceding 90 mine period: negaive informaion (Index< ), non informaion (abs(index)<0.000) and posiive informaion (Index>0.0060). All independen variables are measred over e same 90-mine inerval. rice-vwa is e raio of e midpoin of e crren bid-ask qoe divided b e volme-weiged average price. BSell () is a measre of order flow imbalance based on e difference beween b and sell volme, b and sell rnover, or b and sell rades. rading () is a measre of rading acivi based on volme, rnover, or nmber of rades. MSM is e nmber of mines since midnig. anel B: osiive Informaion Regressions Model 3 Index (.37) (.58) (.79) rice-vwa (5.84) (4.0) (6.68) BSell (volme) (-6.36) BSell (rnover) (-6.0) BSell (rades) (-4.3) rading (volme) (-4.40) rading (rnover) (-3.77) rading (rades) (-5.77) MSM (.0) (.64) (0.90) Adj. R-sqare

39 able 3 Regressions of nex-da sock rerns on lagged rading caracerisics Coefficien esimaes (-saisics) from pooled cross-secional and ime series regressions of marke-adjsed nex-da sock rerns on lagged index fres rerns and rading caracerisics. e dependen variable, ADJR, is e nex-da marke adjsed rern for e sock following a informaion even. We define ree pes of informaion evens based on e rern of a relevan index fres over e preceding 90 mine period: negaive informaion (Index< ), non informaion (abs(index)<0.000) and posiive informaion (Index>0.0060). All independen variables are measred over e same 90-mine inerval. rice-vwa is e raio of e midpoin of e crren bid-ask qoe divided b e volme-weiged average price. BSell () is a measre of order flow imbalance based on e difference beween b and sell volme, b and sell rnover, or b and sell rades. rading () is a measre of rading acivi based on volme, rnover, or nmber of rades. MSM is e nmber of mines since midnig. anel C: Non Informaion Regressions Model 3 Index (.43) (.50) (.30) rice-vwa (8.69) (8.36) (8.6) BSell (volme) -0.0 (-.70) BSell (rnover) (-.) BSell (rades) (-.03) rading (volme) (0.0) rading (rnover) 0.89 (5.80) rading (rades) (-3.3) MSM (.03) (0.80) (.) Adj. R-sqare

40 References Adamai and fleiderer, 988, A eor of inrada paerns: volme and price variabili, Review of Financial Sdies,, Brennan, Jagadees, and Swaminaan, 993, Invesmen analsis and e adjsmen of sock prices o common informaion, Review of Financial Sdies, 6, Bodok, J., M. Ricardson and R.F. Wielaw, 994, A ale of ree scools: Insigs on aocorrelaions of sor-orizon rerns, Review of Financial Sdies 7, Bodok, J., M. Ricardson and R.F. Wielaw, 00, arial adjsmen or sale prices: implicaions from sock index and fres rerns, Review of Financial Sdies5, Calmers, Edelen, and Kadlec, 00, "On e perils of secri pricing b financial inermediaries: e mal fnd wildcard opion", Jornal of Finance, 56, Cordia, Roll, and Sbramanam, 00, Order imbalance, liqidi, and marke rerns, Jornal of Financial Economics, 65, -30. Cordia and Sbramanam, 004, Order imbalance and individal sock rerns: eor and evidence, Jornal of Financial Economics, 7, Dow J., G. Goron, 997, Noise rading, delegaed porfolio managemen and economic welfare, Jornal of oliical Econom, Ocober Vol 05:5 p Edelen, R., 999, Invesor flows and e assessed performance of open-end mal fnds, Jornal of Financial Economics, 53, Edelen and Kadlec, 005, Isser srpls and e parial-adjsmen of IO prices o pblic informaion, Jornal of Financial Economics, 77, Falkensein, 996, references for sock caracerisics as revealed b mal fnd porfolio oldings, Jornal of Finance, 5, -35. Fiser, L., 966, Some new sock marke indices, Jornal of Bsiness 39, 9-5. Foser and Viswanaan, 993, e effec of pblic informaion and compeiion on rading volme and price volaili, Review of Financial Sdies, 6, Harris and Sclz, 998, e rading profis of SOES bandis, Jornal of Financial Economics, 50, Hasbrock and Sofianos, 993, e rades of marke makers: An empirical analsis of NYSE specialiss, Jornal of Finance, 48,

41 Hasbrock, 003, rading coss and rerns for U.S. eqiies: evidence from dail daa, New York Universi working paper. Hasbrock, 00, Inrada price formaion in US eqi index markes, forcoming Jornal of Finance. Kadlec and aerson, 999, A ransacions daa analsis of nonsncronos rading, Review of Financial Sdies,, Kavajecz and Odders-Wie, 004, ecnical analsis and liqidi provision, forcoming, Review of Financial Sdies 7, Keim, 989, rading paerns, bid-ask spreads, and esimaed secri rerns, Jornal of Financial Economics, 5, Keim and Madaven, 995, Anaom of e rading process: empirical evidence on e beavior of insiional raders, Jornal of Financial Economics, 37, Lee, and Read, 99, Inferring rade Direcion from Inrada Daa, Jornal of Finance 46, pp Lipson and cke, 006, Volaile markes and insiional rading, working paper, Darden Gradae Scool of Bsiness. Lo and MacKinla, 990, An economeric analsis of nonsncronos rading, Jornal of Economerica, 45, 8-. Madavan, 00, VWA sraegies, ransacion erformance, Spring, Nagel, 006, rading sles and rading volme, Sanford Universi working paper. erold, 988, e implemenaion sorfall: paper verss reali Jornal of orfolio Managemen 4,

42 Appendices A. Marke Maker Expecaions Le X denoe e ransformaion F V X = υ ψ =. (a) e random variables ψ, U, and X are join normal = 0 0, N X U υ ψ η υ ψ ψ, (a) so [ ] [ ] 0, Σ Σ = X U X U Eψ [ ] = 0 X U

43 4 4 [ ] ( )( ) ( ) ( ) ( ) ( ) = 0 X U X U = ( ) S w zu w X X U = = = ( ) S w U z w X = =. (a3) [ ] ', Σ Σ Σ = Σ X U Varψ [ ] ( )( ) ( ) ( ) ( ) ( ) = 0 0 ( ) ( ) = ( ) ( ) = = =

44 43 B. Demands in period Firs noe (see Eq. (6)): Ω N FV M ( ) ( Ω )( ) = = ( Ω ) (b) FV N ( ) M ( ) = Ω Ω ( ) = Ω (b) e rader s period objecive is deermined b Eq. (4), wic as firs order condiion w.r.. : φ N FV M ( Ω ) ( E [ ] E [ ] ) α Ω ( E [ ] ) 0 =. (b3) E FV since E [ ψ ] Noe a [ ] 0 = ws = (see Appendix A). Also, [ ] 0 N = E. s, N ( ) φ Ω M ( Ω ) ( Ω ) ( Ω ) ( ) α Ω Ω N M Ω Ω = 0 (b4) ( α Ω φ ( Ω ) ) M N = 0 = M N. (b5) 43

45 C. Expeced compensaion Firs noe: N FV ( ) N Ω = (c) N FV ( ) M = Ω (c) Were FV Γ = is is a cange, from previos Expeced compensaion is φ A E 0 ˆ α M ( ) A E 0 φ FV N ε α Ω N FV ( ) FV φ N φ Ω [ ] E [ ] E α ( σ ) φ A E N σ FV (c3) 4 Componens:

46 45 FV FV Ω FV Ω [ ] = E = E 0 0 σ FV (c4) N N N [ ] Ω N FV σ = ( ) N E = ( Ω ) E 0 0 (c5) N [ ] Ω N FV σ 0 0 ( ) N σ FV E = E = ( Ω ) Ω (c6) Compensaion φ Ω σ N σ σ Ω A σ FV φ σ ( ) N FV ( ) Ω φ Ω φ Ω α ( σ ) N FV 4 4 (c7) ( Ω ) φ ( Ω ) φ Ω φ Ω Ω φ Ω A σ FV α σ N α (c8) 4 4 ( Ω ) φ ( Ω ) φ Ω φ Ω Ω φ Ω A σ FV 4 α σ 4 N α (c9) ( Ω σ ( Ω ) ) φ A FV σ N (c0) 4 45

47 46 46 D. Relaive cos of order compleion δ δ = = M M HYO Π Ω = = Π Ω = δ δ δ δ M M HYO Relaive cos of execed orders ( ) ( ) HYO HYO ˆ ˆ ˆ ˆ (0) ( ) ( ) ( ) HYO HYO ˆ ˆ ˆ ˆ ˆ ˆ ˆ ˆ (0) ( ) ( ) ( ) ( ) HYO HYO ˆ ˆ ˆ ˆ ˆ ˆ ˆ ˆ Relaive cos of nexeced orders ( ) ( ) ( ) M HYO HYO 3 ˆ ˆ ˆ ˆ ˆ ˆ

48 M HYO HYO M ( ˆ ˆ ) ( ) ( ˆ ˆ ˆ ˆ ) ( ) 3 Add e wo residals --- ( ˆ HYO HYO ˆ ˆ ˆ ) ( ) ( ˆ HYO HYO M ˆ ˆ ˆ ) ( ) HYO HYO M ( ˆ ˆ ˆ ˆ ) Wic is zero in expecaion. So, sing po is e same as sing sraig VWA. E. Cos o e porfolio manager Relaive rading coss = ncondiional expecaion of = = M ( VWA ) ( ) E 0 3 M E 0 3 ( ) 47 47

49 48 = N FV ( ) Ω N FV ( ) N Ω E 0 3 N ( ) N Ω = FV E 0 3 (e) Firs erm = E 0 N = E N FV N σ N σ N 0 ε = = 4 (e) (negaive cos means a benefi) Second erm = N FV ( ) = FV N Ω E ε 3 M M Ω N FV were = ( ) = ( ) 3 N dropping erms wi no correlaion, = N N FV Ω N FV ( Ω Ω ) ( ) = E

50 = σ Ω Ω ( Ω ) FV N σ Bo firs and second erms N σ FV σ Ω 4 = Ω ( Ω ) = Ω 0 ( Γ ) ( 4 ( Ω ) ) E ( zu ) E Ω 6 0 A..3 oal cos o e M = σ N 4 Ω Ω φ A ( FV σ N ) 4 ( Ω ) σ Ω σ ( Ω ) FV = σ N A Ω 4 FV ( 4 Ω ( Ω ) φ ( Ω ) ) ( 4 Ω φ ) σ 4 Opimm coice? Le α = ( φ ) 4 lf. en Ω = = f lf 4 l ( f ) /

51 min Ω = N 5 A σ ( 3 Ω 5 Ω ) Ω σ 4 4 FV 0 N = σ ( 3 0 Ω ) Ω σ FV Ω * = 3 0 FV σ N ( σ σ ) N <. es: compensaion less an ne benefi o M? σ N ( Ω σ ( Ω ) σ ) < Ω ( Ω ) A φ Ω FV N σ 4 4 FV ( 4 Ω ( Ω ) Ω ( Ω ) ) 5 4 A < σ N Ω σ FV ( 3 Ω 5 Ω ) 5 4 A < σ N Ω σ FV ( 3 Ω ) 5 Ω ( σ ) 4 A < σ N FV σ N 3 0 ( 3 Ω ) 5 Ω 4 A < σ N σ N A < 4 σ N 3 Ω * 50 50

52 5 5

53 F. rice adjsmen delas Marke clearing prices are N ( ) = V N ( ) = V. (a4) Using Eqs.(5) and (6), M M N ( R ) = M N M φ N V R = V 4 N = φ M N M φ V R N 4. (a5) 5 5

54 53 G. Using a Marke-adjsed rice in VWA is appendix reconsiders e models resls sing a modified VWA a conrols for marke moves. s, in Eq. () of secion.3., compensaion is based on V R M ˆ =. (g) Mos of e analsis follows rog ncanged, excep a FV of Eq. () is reformlaed as ( ws ) ws FV = ψ, (g) As before, FV is e sorce of agenc coss of insiional rading. Wile e marke-adjsed VWA bencmark eliminaes marke rerns as a sorce of exploiable rerns, ere we see a exploiaion opporniies remain. In pariclar, bo pblic ( ψ ws ) and (e rader s raional assessmen of) privae ( ws ) idiosncraic informaion inflence marke prices in a wa a sows p in e rader s compensaion. Of corse, roposiion, wic relaes o marke rerns, is no longer relaven. e remaining proposiions remain ncanged, excep a σ FV will generall be smaller in magnide. 53

55 54 54