Byeong-Je An, Andrew Ang, Turan Bali and Nusret Cakici The Joint Cross Section of Stocks and Options

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1 Byeong-Je An Andrew Ang Turan Bal and Nusre Cakc The Jon Cross Secon of Socks and Opons DP 10/

2 The Jon Cross Secon of Socks and Opons * Byeong-Je An Columba Unversy Andrew Ang Columba Unversy and NBER Turan G. Bal Georgeown Unversy Nusre Cakc ** Fordham Unversy Ths Verson: 7 Ocober 2013 Keywords: mpled volaly rsk premums predcably shor-erm momenum JEL Classfcaon: G10 G11 C13. * We hank he edor Cam Harvey an assocae edor and hree referees for her exremely helpful commens and suggesons. We hank Reena Aggarwal Allan Eberhar Ncolae Garleanu Larry Glosen Bob Hodrck Mchael Johannes George Panayoov Tyler Shumway Mee Soner Davd Wenbaum Luren Wu Yuhang Xng and semnar parcpans a he Amercan Fnance Assocaon meengs ETH- Zurch Federal Reserve Bank of New York and Georgeown Unversy for helpful commens and dscussons. Addonal resuls are avalable n an nerne appendx ha can be obaned by conacng he auhors. An and Ang hank Nespar and he Program for Fnancal Sudes for fnancal suppor. Columba Busness School 3022 Broadway 6A Urs New York NY Phone: (917) Emal: ba2306@columba.edu. Columba Busness School 3022 Broadway 413 Urs New York NY Phone: (212) Emal: aa610@columba.edu. Correspondng auhor. McDonough School of Busness Georgeown Unversy Washngon D.C Phone: (202) Fax: (202) E-mal: gb27@georgeown.edu. ** Graduae School of Busness Fordham Unversy 113 Wes 60h Sree New York NY Phone: (212) Emal: cakc@fordham.edu.

3 The Jon Cross Secon of Socks and Opons ABSTRACT Socks wh large ncreases n call mpled volales over he prevous monh end o have hgh fuure reurns whle socks wh large ncreases n pu mpled volales over he prevous monh end o have low fuure reurns. Sorng socks ranked no decle porfolos by pas call mpled volales produces spreads n average reurns of approxmaely 1% per monh and he reurn dfferences perss up o sx monhs. The cross secon of sock reurns also predcs opon-mpled volales wh socks wh hgh pas reurns endng o have call and pu opon conracs whch exhb ncreases n mpled volaly over he nex monh bu wh decreasng realzed volaly. These predcably paerns are conssen wh raonal models of nformed radng.

4 1. Inroducon Opons are redundan asses only n an dealzed world of complee markes wh no ransacons coss perfec nformaon and no resrcons on shorng. No surprsngly snce n he real world none of hese assumpons hold opons are no smply funcons of underlyng sock prces and rsk-free secures. 1 We show ha he cross secon of opon volales conans nformaon ha forecass he cross secon of expeced sock reurns and he cross secon of sock-level characerscs forecass opon mpled volales. In he drecon of opon volales predcng sock reurns we fnd ha socks wh call opons whch have experenced ncreases n mpled volales over he pas monh end o have hgh reurns over he nex monh. Pus conan ndependen nformaon from call opons especally pus whose mpled volales move oppose o he drecon predced by pu-call pary. Afer conrollng for movemens n call mpled volales ncreases n pu opon volales predc decreases n nex-monh sock reurns. The srengh and perssence of hs predcably for sock reurns from he cross secon of opon volales s remarkable for several reasons. Frs he nnovaon n mpled volales can be consdered o be a very smple measure of news arrvals n he opon marke. Whle sronges for he nex-monh horzon he predcably persss a leas up o sx monhs. The predcably a he sandard monhly horzon suggess he predcably s unlkely due o mcrosrucure radng effecs. In conras mos of he prevous leraure nvesgang lead-lag effecs of opons versus sock markes focuses on nra-day or daly frequences. These hgh frequency sudes largely fnd ha boh he opon and sock markes quckly reac o news and ha a daly frequences or hgher opons and socks are farly prced relave o each oher. 2 Second he predcably s sascally very srong and economcally large. Decle porfolos formed on pas changes n call opon volaly have a spread of approxmaely 1% per monh n boh raw reurns and alphas compued usng common sysemac facor models. Socks sored on pas ncreases n her pu mpled volales afer conrollng for mpled call volales exhb spreads n average reurns of greaer han 1% per monh beween he exreme decle porfolos. The predcably of sock reurns by 1 Many heorecal models jonly prcng opons and underlyng asses n ncomplee markes have ncorporaed many of hese real-world frcons. See Deemple and Selden (1991) Back (1993) Cao (1999) Burasch and Jlsov (2006) and Vanden (2008) among ohers. 2 A he daly or nra-day frequences Manaser and Rendleman (1982) Bhaacharya (1987) and Anhony (1988) fnd ha opons predc fuure sock prces. Flemng Osdek and Whaley (1996) documen dervaves lead he underlyng markes usng fuures and opons on fuures. On he oher hand Sephan and Whaley (1990) and Chan Chung and Johnson (1993) fnd sock markes lead opon markes. Chakravary Gulen and Mayhew (2004) fnd ha boh sock and opon markes conrbue o prce dscovery whle Muravyev Pearson and Broussard (2013) fnd ha prce dscovery occurs only n he sock marke. 1

5 opon nnovaons s also robus n several subsamples. Whereas many cross-seconal sraeges have reversed sgn or become much weaker durng he fnancal crss he ably of opon volales o predc reurns s sll seen n recen daa. The predcably from opons o sock reurns s conssen wh economes where nformed raders choose he opon marke o rade frs such as hose developed by Chowdhry and Nanda (1991) and Easley O Hara and Srnvas (1998). Ths causes he opon marke o lead he sock marke where nformed radng does no predomnae. Informed nvesors however would no always exclusvely choose jus one marke o rade. In a nosy raonal expecaons model of nformed radng n boh sock and opon markes (dealed n Appendx A) we show ha nformed radng conemporaneously moves boh opon and sock markes. Informed raders who receve news abou fuure frm cashflows can rade eher socks opons or boh and do so dependng on he relave sze of nose radng presen n each marke. Marke makers who are allowed o rade boh sock and opon markes ensure ha sock and opon prces sasfy arbrage bounds. The presence of nose raders n boh sock and opon markes allows nformed raders o dsguse her rades so he prces do no mmedaely adjus o fully-revealng effcen prces whch would resul n he absence of nose raders. The model mples ha opon volales can predc fuure sock reurns. The model also ndcaes ha he predcably should be hghes when he underlyng volumes n boh sock and opon markes are larges whch we confrm n emprcal ess. Imporanly he model shows ha nformed radng also gves rse o sock-level nformaon predcng opon reurns. Thus boh drecons of predcably from opon markes o sock markes and vce versa arse smulaneously. Conssen wh he model we also uncover evdence of reverse dreconal predcably from sock prce varables o opon markes. Many of he varables long known o predc sock reurns also predc opon mpled volales. 3 A very smple predcor s he pas reurn of a sock: socks wh hgh pas reurns over he prevous monh end o have call opons ha exhb ncreases n volaly over he nex monh. In parcular socks wh abnormal reurns of 1% relave o he CAPM end o see call (pu) mpled volales ncrease over he nex monh by approxmaely 4% (2%). The model also predcs ha pas sock reurns predc fuure ncreases n opon volales and fuure decreases n realzed sock reurns whch we confrm n daa. The nuon s ha nformed radng oday causes prces o parally adjus and hs resolves some of he fuure uncerany n frm cashflows. Snce some nformaon s revealed n prces fuure realzed volaly of sock prces decreases. The 3 Ths predcably s nconssen wh sandard arbrage-free opon prcng models whch a long leraure has also shown. The earler papers n hs leraure nclude Fglewsk (1989) and Longsaff (1995). More recenly see Goyal and Sareo (2009) and Cao and Han (2013). 2

6 predcably of opon volales s sronger n socks whch exhb a lower degree of predcably and socks whose opons are harder o hedge conssen wh oher raonal models. Behavoral over-reacon heores predc ha opon mpled volales should ncrease ogeher wh oher measures of uncerany such as earnngs dsperson. We fnd hs s no he case. Our fndngs are relaed o a recen leraure showng ha opon prces conan predcve nformaon abou sock reurns. Cao Chen and Grffn (2005) fnd ha merger nformaon hs he call opon marke pror o he sock marke bu focus only on hese specal corporae evens. Bal and Hovakman (2009) Cremers and Wenbaum (2010) and Xng Zhang and Zhao (2010) use nformaon n he cross secon of opons ncludng he dfference beween mpled and realzed volales pu-call pary devaons and rsk-neural skewness. Johnson and So (2012) show ha he rao of opon marke volume o equy marke volume predcs sock reurns. We conrol for all of hese varables n examnng he predcably of sock reurns by lagged nnovaons n call and pu opon volales. Our paper s relaed o Cremers and Wenbaum (2010) who examne he predcably of sock reurns from volaons of pu-call pary. In passng hey examne he predcably of jon call and pu volaly changes on sock reurns bu do no separaely examne her effecs. They nerpre her fndngs of sock reurn predcably by opon nformaon as nformed nvesors preferrng o rade frs n opon markes. Lke Cremers and Wenbaum our resuls are conssen wh nformed radng sores as we relae changes n opon volales o conemporaneous changes n opon volume. Dfferen o Cremers and Wenbaum we show ha he predcably of sock reurns by pas changes n opon mpled volales arses n a model of nformed radng whch predcs ha here should be boh predcably from he cross secon of opon o sock markes and vce versa. Oher relaed sudes focus on predcng opon reurns opon radng volume or he opon skew n he cross secon. Goyal and Sareo (2009) show ha dela-hedged opons wh a large posve dfference beween realzed and mpled volaly have low average reurns. Roll Schwarz and Subrahmanyam (2009) examne he conemporaneous bu no predcve relaon beween opons radng acvy and sock reurns. Denns and Mayhew (2002) documen cross-seconal predcably of rsk-neural skewness bu do no examne he cross secon of mpled volales. In conras o hese sudes we focus on he srong predcve power of he lagged sock reurn n he cross secon whch o our knowledge has been examned only n he conex of opons on he aggregae marke by Amn Coval and Seyhun (2004). We also fnd many of he usual suspecs n he commonly used sock characerscs ha predc sock reurns also predc he cross secon of opon-mpled volales lke book-o-marke raos momenum and llqudy measures. 3

7 The res of he paper s organzed as follows. Secon 2 covers he daa and varable defnons. Secons 3 and 4 examne he predcve power of opon mpled volaly changes on he cross secon of sock reurns usng sock porfolos and cross-seconal regressons respecvely. Secon 5 nvesgaes he reverse drecon of predcably from sock reurns o realzed and mpled volales. Secon 6 concludes. 2. Daa 2.1. Impled Volales The daly daa on opon mpled volales are from OponMercs. The OponMercs Volaly Surface compues he nerpolaed mpled volaly surface separaely for pus and calls usng a kernel smoohng algorhm usng opons wh varous srkes and maures. The underlyng mpled volales of ndvdual opons are compued usng bnomal rees ha accoun for he early exercse of ndvdual sock opons and he dvdends expeced o be pad over he lves of he opons. The volaly surface daa conan mpled volales for a ls of sandardzed opons for consan maures and delas. A sandardzed opon s only ncluded f here exss enough underlyng opon prce daa on ha day o accuraely compue an nerpolaed value. The nerpolaons are done each day so ha no forwardlookng nformaon s used n compung he volaly surface. One advanage of usng he Volaly Surface s ha avods havng o make poenally arbrary decsons on whch srkes or maures o nclude n compung an mpled call or pu volaly for each sock. In our emprcal analyses we use call and pu opons mpled volales wh a dela of 0.5 and an expraon of 30 days. For robusness we also examne oher expraons especally of 91 days whch are avalable n he nerne appendx. Our sample s from January 1996 o December In he nerne appendx we also show ha our resuls are smlar usng mpled volales of acual opons raher han he Volaly Surface. Table 1 conans descrpve sascs of our sample. Panel A repors he average number of socks per monh for each year from 1996 o There are 1261 socks per monh n 1996 rsng o 2312 socks per monh n We repor he average and sandard devaon of he end-of-monh annualzed call and pu mpled volales of a-he-money 30-day maures whch we denoe as CVOL and PVOL respecvely. Boh call and pu volales are hghes durng 2000 and 2001 whch concdes wh he large declne n sock prces parcularly of echnology socks durng hs me. Durng he 4

8 recen fnance crss n we observe a sgnfcan ncrease n average mpled volales from around 40% o 60% for boh CVOL and PVOL Predcve Varables We oban underlyng sock reurn daa from CRSP and accounng and balance shee daa from COMPUSTAT. We consruc he followng facor loadngs and frm characerscs assocaed wh underlyng sock markes ha are wdely known o forecas he cross secon of sock reurns: 5 Bea: Followng Scholes and Wllams (1977) and Dmson (1979) we ake no accoun nonsynchronous radng by esmang an exended verson of he marke model a he daly frequency o oban he monhly bea of an ndvdual sock: R d rf d 1 ( Rm d 1 rf d 1 ) 2 ( Rm d rf d ) 3 ( Rm d 1 rf d 1) d (1) where R d s he reurn on sock on day d m d R s he marke reurn on day d and r f d s he rsk-free rae on day d. We ake R md o be he CRSP daly value-weghed ndex and r fd o be he Ibboson rskfree rae. We esmae equaon (1) for each sock usng daly reurns over he pas monh. The sum of he esmaed slope coeffcens ˆ ˆ ˆ s he marke bea of sock n monh. The adjusmen of beas o non-synchronous radng has lle effec as we fnd very smlar resuls usng regular beas. Sze: Frm sze s measured by he naural logarhm of he marke value of equy (sock prce mulpled by he number of shares ousandng n mllons of dollars) a he end of he monh for each sock. Book-o-Marke Rao (BM): Followng Fama and French (1992) we compue a frm s book-o-marke rao n monh usng he marke value of s equy a he end of December of he prevous year and he 4 There are many reasons why pu-call pary does no hold as documened by Ofek Rchardson and Whelaw (2004) and Cremers and Wenbaum (2010) among ohers. In parcular he exchange-raded opons are Amercan and so pu-call pary only holds as an nequaly. The mpled volales we use are nerpolaed from he Volaly Surface and do no represen acual ransacons prces whch n opons markes have large bd-ask spreads and non-synchronous rades. These ssues do no affec he use of our opon volales as we use predcve nsrumens observable a he begnnng of each perod. 5 Easley Hvdkjaer and O Hara (2002) nroduce a measure of he probably of nformaon-based radng PIN and show emprcally ha socks wh hgher probably of nformaon-based radng have hgher reurns. Usng PIN as a conrol varable does no nfluence he sgnfcanly posve (negave) lnk beween he call (pu) volaly nnovaons and expeced reurns. We also examne he effec of sysemac coskewness followng Harvey and Sddque (2000). Includng coskewness does no affec our resuls eher. See he nerne appendx. 5

9 book value of common equy plus balance-shee deferred axes for he frm s laes fscal year endng n pror calendar year. To avod ssues wh exreme observaons we follow Fama and French (1992) and Wnsorze he book-o-marke raos a he 0.5% and 99.5% levels. Momenum (MOM): Followng Jegadeesh and Tman (1993) he momenum varable for each sock n monh s defned as he cumulave reurn on he sock over he prevous 11 monhs sarng 2 monhs ago o avod he shor-erm reversal effec.e. momenum s he cumulave reurn from monh 12 o monh 2. Illqudy (ILLIQ): We use he Amhud (2002) defnon of llqudy and for each sock n monh defne llqudy o be he rao of he absolue monhly sock reurn o s dollar radng volume: ILLIQ R / VOLD radng volume of sock n dollars. where R s he reurn on sock n monh and VOLD s he monhly Shor-erm reversal (REV): Followng Jegadeesh (1990) Lehmann (1990) and ohers we defne shorerm reversal for each sock n monh as he reurn on he sock over he prevous monh from 1 o. Realzed volaly (RVOL): Realzed volaly of sock n monh s defned as he sandard devaon of daly reurns over he pas monh RVOL var( R d ). We denoe he monhly frs dfferences n RVOL as ΔRVOL. The second se of predcve varables s from opon markes: Impled volaly nnovaons: We defne mpled volaly nnovaons as he change n call and pu mpled volales whch we denoe as ΔCVOL and ΔPVOL respecvely: 6 CVOL CVOL CVOL 1 PVOL PVOL PVOL 1. (2) Whle he frs dfference of mpled volales s a very aracve measure because s smple gnores he fac ha mpled volales are predcable n boh he me seres (mpled volales exhb 6 As an addonal robusness check we also consder proporonal changes n CVOL and PVOL and fnd very smlar resuls. The resuls from he percen changes n call and pu mpled volales (%ΔCVOL %ΔPVOL) are avalable n he nerne appendx. 6

10 sgnfcan me-seres auocorrelaon) and cross secon (mpled volales are predcable usng crossseconal sock characerscs). In he nerne appendx we consder wo oher measures accounng for hese dmensons of predcably and fnd ha volaly nnovaons consruced from boh me-seres and cross-seconal models also predc sock reurns. Call/Pu (C/P) volume: The relaon beween opon volume and underlyng sock reurns has been suded n he leraure wh mxed fndngs by Sephan and Whaley (1990) Amn and Lee (1997) Easley O Hara and Srnvas (1998) Chan Chung and Fong (2002) Cao Chen and Grffn (2005) and Pan and Poeshman (2006) and ohers. Followng Pan and Poeshman (2006) our frs measure of opon volume s he rao of call/pu opon radng volume over he prevous monh. Call/Pu open neres (C/P OI): A second measure of opon volume s he rao of open neress of call opons o pu opons. Realzed-mpled volaly spread (RVOL IVOL): Followng Bal and Hovakman (2009) and Goyal and Sareo (2009) we conrol for he dfference beween he monhly realzed volaly (RVOL) and he average of he a-he-money call and pu mpled volales denoed by IVOL (usng he Volaly Surface sandardzed opons wh a dela of 0.50 and maury of 30 days). Bal and Hovakman (2009) show ha socks wh hgh RVOL IVOL spreads predc low fuure sock reurns. Goyal and Sareo (2009) fnd smlar negave effec of he RVOL IVOL spread for fuure opon reurns. Rsk-neural skewness (QSKEW): Followng Conrad Dmar and Ghysels (2012) and Xng Zhang and Zhao (2010) we conrol for rsk-neural skewness defned as he dfference beween he ou-of-he-money pu mpled volaly (wh dela of 0.20) and he average of he a-he-money call and pu mpled volales (wh delas of 0.50) boh usng maures of 30 days. Xng Zhang and Zhao (2010) show ha socks wh hgh QSKEW end o have low reurns over he followng monh. On he oher hand Conrad Dmar and Ghysels (2012) repor he oppose relaon usng a more general measure of rsk-neural skewness based on Baksh Kapada and Madan (2003) whch s derved usng he whole cross secon of opons. Correlaons of Volaly Innovaons Panel B of Table 1 presens he average frm-level cross correlaons of he level and nnovaons n mpled and realzed volales. The average correlaon beween he levels of call and pu mpled volales (CVOL and PVOL) s 92%. Ths hgh correlaon reflecs a general volaly effec reflecng 7

11 ha when curren sock volaly ncreases mpled volales of all opon conracs across all srkes and maures also end o rse. Noe ha f pu-call pary held exacly hen he correlaon of CVOL and PVOL would be one. Pu-call pary holds approxmaely (bu no always as Ofek Rchardson and Whelaw (2004) and Cremers and Wenbaum (2010) explo) so o examne he ncremenal predcve power of pu volales we wll conrol for he general level volaly effec. 7 The perssence of he level volaly facor s also refleced n he hgh correlaon (66%) of pas realzed volaly wh boh CVOL and PVOL. The frs dfferences n mpled volales ΔCVOL and ΔPVOL have a lower correlaon of 58% han he 92% correlaon beween he levels of CVOL and PVOL The posve correlaon beween ΔCVOL and ΔPVOL also reflecs he common componen n boh call and pu volales. The changes n mpled volales are no correlaed wh eher RVOL or ΔRVOL wh correlaons of ΔCVOL wh RVOL and ΔRVOL beng 0.02 and 0.08 respecvely. The correlaons of ΔPVOL wh RVOL and ΔRVOL are also low a 0.03 and 0.10 respecvely. Ths shows ha he forward-lookng CVOL and PVOL esmaes are reacng o more han jus pas volaly capured by RVOL and ha nnovaons n mpled volales represen new nformaon no capured by backward-lookng volaly measures. 3. Reurns on Porfolos Sored by Opon Impled Volales 3.1. Unvarae Porfolo Sors Porfolos Sored by CVOL Panel A of Table 2 shows ha socks ha have pas hgh changes n mpled call volales have hgh fuure reurns. We form decle porfolos ranked on ΔCVOL rebalanced every monh. Porfolo 1 (Low ΔCVOL) conans socks wh he lowes changes n call mpled volales n he prevous monh and Porfolo 10 (Hgh ΔCVOL) ncludes socks wh he hghes changes n call mpled volales n he prevous monh. We equal wegh socks n each decle porfolo and rebalance monhly. Panel A of Table 2 shows he average raw reurn of socks n decle 1 wh he lowes ΔCVOL s 0.29% per monh and hs monooncally ncreases o 1.38% per monh for socks n decle 10. The dfference n average raw reurns beween decles 1 and 10 s 1.09% per monh wh a hghly sgnfcan Newey-Wes -sasc of Ths ranslaes o a monhly Sharpe rao of 0.26 and an annualzed Sharpe rao of 0.90 for a sraegy gong long Hgh ΔCVOL socks and shorng Low ΔCVOL socks. 7 In he smplfed model of Appendx A pu and call opons are equvalen secures because we assume bnomal payoffs. 8

12 The dfferences n reurns beween decles 1 and 10 are very smlar f we rsk adjus usng he CAPM a 1.04% per monh and he Fama-French (1993) model [FF3 hereafer] ncludng marke sze and book-o-marke facors a 1.00% per monh. In he fnal column we do a characersc mach smlar o Danel and Tman (1997) and Danel e al. (1997). The Danel and Tman (1997) characersc mached procedure pars each sock wh a machng porfolo of frms ha have approxmaely he same book-o-marke raos and sze. We use 100 porfolos formed from he nersecon of 10 porfolos sored on sze and 10 porfolos sored on book-o-marke raos followng Danel and Tman (1997). Ths reduces he decle 1 and 10 dfference o 0.86% per monh (-sasc of 2.87) bu hs s sll boh economcally large and sascally sgnfcan. Porfolos Sored by PVOL In Panel B of Table 1 we form decle porfolos ranked on ΔPVOL rebalanced every monh. Porfolo 1 (Low ΔPVOL) conans socks wh he lowes changes n pu mpled volales n he prevous monh and Porfolo 10 (Hgh ΔPVOL) ncludes socks wh he hghes changes n pu mpled volales n he prevous monh. Mos of he reurns o he ΔPVOL porfolos are approxmaely he same wh a noable dfference for he socks wh he hghes changes n pas mpled pu volales porfolo 10. The average raw reurn dfference beween Hgh ΔPVOL and Low ΔPVOL decles s 0.42% per monh wh a sgnfcan Newey-Wes -sasc of The CAPM and FF3 alpha dfferences beween decles 1 and 10 are respecvely 0.46% and 0.50% per monh wh he -sascs of 2.14 and As shown n he las column of Panel B he characersc mached porfolos of ΔPVOL also generae a negave and sgnfcan reurn dfference 0.42% per monh wh a -sasc of The posve (negave) reurn spreads n he ΔCVOL (ΔPVOL) porfolos are conssen wh an nformed radng sory. An nformed bullsh rader who has good nformaon ha a sock s lkely o go up nex perod bu he marke does no compleely reac o he rades of ha nformed nvesor hs perod can buy a call whch ncreases call opon volales hs perod and subsequenly he sock prce goes up he followng perod. A smlar sory holds for a bearsh nformed nvesor beng a sock wll decrease n value can buy a pu so ncreases n pu mpled volales forecas decreases n nex-monh sock reurns. Pu and call opons however are lnked by pu-call pary. Alhough pu-call pary s only approxmae as he opons are Amercan some socks pay dvdends and volaons of pu-call pary do occur ncreases n call mpled volales are generally assocaed wh ncreases n pu mpled volales. Ths causes a large common componen n all opon volales; hs s confrmed n Table 1 whch shows ha ΔCVOL and ΔPVOL have a correlaon of Thus alhough an nformed rader 9

13 recevng posve news could buy a call hs perod whch ends o ncrease call volales or sell a pu whch ends o decrease pu volales call and pu volales end no o move n oppose drecons especally ousde arbrage bounds. The large common volaly componen s perhaps responsble for some of he weaker predcably of ΔPVOL compared o he ΔCVOL porfolo sors. To solae he predcably of ΔPVOL compared o ΔCVOL (and also vce versa) we should conrol for he overall mpled volaly level. A rough way o look a he ncremenal predcve power of ΔPVOL conrollng for he overall mpled opon level s o subrac he change n mpled call volales ΔCVOL. Porfolos Sored by PVOL CVOL Panel C of Table 2 presens resuls from decle porfolos ranked on ΔPVOL ΔCVOL rebalanced every monh. Porfolo 1 (Low ΔPVOL ΔCVOL) conans socks wh he lowes spread beween ΔPVOL and ΔCVOL n he prevous monh and Porfolo 10 (Hgh ΔPVOL ΔCVOL) ncludes socks wh he hghes spread beween ΔPVOL and ΔCVOL n he prevous monh. Movng from decles 1 o 10 average raw reurns on he ΔPVOL ΔCVOL porfolos decrease from 1.81% o 0.13% per monh. The dfference n average raw reurns beween decles 1 and 10 s 1.68% per monh wh a hghly sgnfcan Newey-Wes -sasc of The dfferences n rsk-adjused reurns beween decles 1 and 10 are very smlar as well wh a CAPM alpha dfference of 1.66% per monh (-sasc = 6.67) and a FF3 alpha dfference of 1.65% per monh (-sasc = 6.49). As shown n he las column of Panel C he characersc mached porfolos of ΔPVOL ΔCVOL also generae a negave and sgnfcan reurn dfference 1.44% per monh wh a -sasc of 5.31 beween he exreme decles 1 and 10. Smply akng he dfference beween ΔCVOL and ΔPVOL s a crude way of conrollng for an overall volaly effec. We wsh o es he predcably of ΔCVOL and ΔPVOL when jonly conrollng for boh effecs we expec o see sock reurns ncrease mos for hose socks where bullsh nvesors drve upwards call opon volales and smulaneously drve downwards pu opon volales. We can jonly conrol for ΔCVOL and ΔPVOL effecs n porfolos by consrucng bvarae porfolo sors whch we urn o now Bvarae Porfolo Sors Predcve Ably of CVOL Conrollng for PVOL 10

14 In order o examne he predcve power of ΔCVOL conrollng for ΔPVOL we need o creae porfolos ha exhb dfferences n ΔCVOL wh approxmaely he same levels of ΔPVOL. We do hs n Panel A of Table 3. We frs perform a sequenal sor by creang decle porfolos ranked by pas ΔPVOL. 8 Then whn each ΔPVOL decle we form a second se of decle porfolos ranked on ΔCVOL. Ths creaes a se of porfolos wh smlar pas ΔPVOL characerscs wh spreads n ΔCVOL and hus we can examne expeced reurn dfferences due o ΔCVOL rankngs conrollng for he effec of ΔPVOL. We hold hese porfolos for one monh and hen rebalance a he end of he monh. Table 3 Panel A repors he monhly percenage raw reurns of hese porfolos. As we move across he columns n Panel A he reurns generally ncrease from low o hgh ΔCVOL. The larges average porfolo reurns are found near he op rgh-hand corner of Panel A conssen wh nformed nvesors radng n opon markes oday o generae large posve ΔCVOL and large negave ΔPVOL changes whch predc sock prce movemens nex perod. Conversely he mos negave porfolo reurns le n he boom lef-hand corner where he larges ΔPVOL changes and he mos negave ΔCVOL movemens predc fuure decreases n sock prces. In a gven ΔPVOL decle porfolo we can ake he dfferences beween he las and frs ΔCVOL reurn decles. We hen average hese reurn dfferenals across he ΔPVOL porfolos. Ths procedure creaes a se of ΔCVOL porfolos wh nearly dencal levels of ΔPVOL. Thus we have creaed porfolos rankng on ΔCVOL bu conrollng for ΔPVOL. If he reurn dfferenal s enrely explaned by ΔPVOL no sgnfcan reurn dfferences wll be observed across ΔCVOL decles. These resuls are repored n he column called ΔCVOL10 ΔCVOL1. All of hese reurn dfferences are around 1% per monh or above and hey are hghly sascally sgnfcan as well. Panel A of Table 3 shows ha he average raw reurn dfference beween he Hgh ΔCVOL and Low ΔCVOL decles s 1.38% per monh wh a -sasc of The average FF3 alpha dfference beween he frs and enh ΔCVOL decles averaged across he ΔPVOL porfolos s 1.36% per monh wh a -sasc of I s possble o consruc bvarae porfolos rankng on ΔCVOL and ΔPVOL based on ndependen sors whch are repored n he nerne appendx. Brefly he reurn dfferences produced usng ndependen sors are larger han he ones repored n Table 3. Conrollng for ΔPVOL he average dfference n reurns (FF3 Alphas) beween exreme ΔCVOL decle porfolos s 1.81% (1.80%) per monh. Conrollng for ΔCVOL he average dfference n reurns (FF3 Alphas) beween exreme ΔPVOL decle porfolos s 1.27% ( 1.26%) per monh. 9 If we augmen he Fama-French (1993) regresson wh addonal facors for momenum and shor-erm reversals he alphas are almos unchanged. These numbers are avalable n he nerne appendx. 11

15 Predcve Ably of PVOL Conrollng for CVOL Panel B of Table 3 repeas he same exercse as Panel A bu performs a sequenal sor frs on ΔCVOL and hen on ΔPVOL. Ths produces porfolos wh dfferen ΔPVOL rankngs afer conrollng for he nformaon conaned n ΔCVOL and allows us o examne he predcve ably of ΔPVOL conrollng for ΔCVOL. Ths se of sequenal sors produces slghly lower reurns n absolue value han Panel A reflecng he smaller spreads n he raw ΔPVOL sors (see Table 2) bu hey are sll economcally very large and hghly sascally sgnfcan. In Panel B we observe he negave relaon beween ncreasng ΔPVOL and lower average reurns n every ΔCVOL decle. Whn each ΔCVOL decle he average reurn dfferences beween he Hgh ΔPVOL and Low ΔPVOL porfolos (ΔPVOL10 ΔPVOL1) are n he range of 0.81% o 1.69% per monh wh he Newey-Wes -sascs rangng from 2.21 o 4.47 wh only wo excepons. The excepons are decles 4 and 6 where he average reurn dfferences beween he hgh and low ΔPVOL decles are sll negave bu he -sascs are sascally nsgnfcan. The las wo rows of Panel B average he dfferences beween he frs and enh ΔPVOL decles across he ΔCVOL decles. Ths summarzes he reurns o ΔPVOL afer conrollng for ΔCVOL. The average reurn dfference s 1.04% per monh wh a -sasc of The average dfference n FF3 alphas s very smlar a 1.06% per monh wh a -sasc of Thus here s a srong negave relaon beween ΔPVOL and sock reurns n he cross secon afer akng ou he effec of he common volaly movemens due o ΔCVOL. In boh panels of Table 3 we repor he change n volume and open neres of calls and pus. Call volume and open neres end o ncrease wh he change n call mpled volales. Ths s also rue for pu volume and open neres. Ths s conssen wh he nerpreaon ha he ncrease n mpled volales may be due o nformed nvesor demand. Ths ncreased demand and he conemporaneous effec on opon volales may be due o he radng of opons by ceran nvesors wh prvae nformaon whch s borne ou nex perod. Appendx A presens a model along hese lnes and our resuls are conssen wh hs nosy raonal expecaons model of nformed radng n boh opons and sock markes Characerscs of ΔCVOL and ΔPVOL Porfolos To hghlgh he frm characerscs rsk and skewness arbues of oponable socks n he porfolos of ΔCVOL and ΔPVOL Table 4 presens descrpve sascs for he socks n he varous decles. The decle porfolos n Table 4 are formed by sorng oponable socks based on ΔCVOL conrollng for ΔPVOL (Panel A) and ΔPVOL conrollng for ΔCVOL (Panel B) formed as descrbed n he prevous 12

16 secon. In each monh we record he medan values of varous characerscs whn each porfolo. These characerscs are all observable a he me he porfolos are formed. Table 4 repors he average of he medan characersc values across monhs of: marke bea (BETA) log marke capalzaon (SIZE) he book-o-marke rao (BM) he cumulave reurn over he 12 monhs pror o porfolo formaon (MOM) he reurn n he porfolo formaon monh (REV) he Amhud (2002) llqudy rao (ILLIQ) he realzed skewness (SKEW) he co-skewness (COSKEW) and he rsk-neural skewness (QSKEW). 10 The second columns n each panel repor he nex-monh average reurn. In Panel A of Table 4 as we move from he low ΔCVOL o he hgh ΔCVOL decle he average reurn on ΔCVOL porfolos ncreases from 0.27% o 1.65%. The reurn spread beween he exreme decle porfolos s 1.38% per monh wh a -sasc of Conrollng for ΔPVOL has produced a larger spread beween he decle 10 and 1 reurns of 1.09% n Table 2 conssen wh ΔCVOL and ΔPVOL represenng dfferen effecs. In Panel A of Table 4 he dfference n FF3 alphas beween he decle porfolos 1 and 10 s 1.36% per monh wh a -sasc of Conssen wh here beng lle dfference n he raw reurn spread versus he FF3 alpha spread here are no dscernble paerns of marke BETA sze and book-o-marke raos across he porfolos. Illqudy also canno be an explanaon as he ILLIQ loadngs are U-shaped across he ΔCVOL decles. In fac socks wh he mos negave and larges changes n ΔCVOL end o be he mos lqud socks. There s however a srong reversal effec wh socks n he low ΔCVOL decle havng he hghes pas one-monh reurn of 3.87% and socks n he hgh ΔCVOL decle havng he lowes pas onemonh reurn of 4.06%. In he nerne appendx we consruc a fve-facor model whch augmens he Fama-French (1993) model wh a momenum facor (see Carhar 1997) and a shor-erm reversal facor. The dfference n average reurns beween he low ΔCVOL and hgh ΔCVOL decle conrollng for he fve facors s 1.37% per monh wh a -sasc of Thus he reurn dfferences o ΔCVOL are no due o shor-erm reversals. We nvesgae wheher he skewness arbues of oponable socks provde an explanaon for he hgh reurns of socks wh large pas changes n ΔCVOL n he las hree columns of Table 4. Panel A shows here are no ncreasng or decreasng paerns across he ΔCVOL decles for realzed skewness (SKEW) or sysemac skewness (COSKEW). There s n conras a pronounced paern of decreasng rsk-neural skewness (QSKEW) movng from 6.28 for he frs ΔCVOL decle o 2.25 for he enh ΔCVOL decle. QSKEW s compued as he spread beween he mpled volales of ou-of-he-money 10 SKEW and COSKEW are compued usng daly reurns over he pas one year. Defnons of all oher varables are gven n Secon 2. As dscussed n he nerne appendx he calculaon of COSKEW follows Harvey and Sddque (2000) where we regress sock reurns on he marke and he squared marke reurns. The slope coeffcen on he squared marke reurn s COSKEW of Harvey and Sddque (2000). 13

17 pus and a-he-money calls. Decreasng QSKEW across he ΔCVOL decles s equvalen o hese socks experencng smulaneous declnes n pas pu volales as ΔCVOL ncreases. Ths s conssen wh nformed radng where nformed bullsh nvesors wh a hgh degree of confdence n fuure prce apprecaon buy calls and sell pus. Below n cross-seconal regressons we wll conrol for QSKEW along wh oher regressors n examnng ΔCVOL and ΔPVOL predcably. In Panel B of Table 4 we repor smlar descrpve sascs for he porfolos sored on ΔPVOL afer conrollng for ΔCVOL. Lke he ΔCVOL porfolos n Panel A we observe no obvous paerns n BETA SIZE BM or ILLIQ whch can explan he reurns of he ΔPVOL porfolos whch decrease from 1.39% for socks wh he lowes pas ΔPVOL o 0.35% for socks wh he hghes pas ΔPVOL. The spread beween decles 1 and 10 s 1.04% per monh wh a hghly sgnfcan -sasc of The dfference n FF3 alphas beween he exreme decles s 1.06% per monh wh a -sasc of Lke Panel A here s a srong paern of ncreasng pas reurns as we move across he ΔPVOL decles. Pas REV however goes n he same drecon as he nex-monh reurns ncreasng from 5.67% for he frs ΔPVOL decle (wh a nex-monh reurn of 1.39%) o 6.52% for he enh ΔPVOL decle (wh a nex-monh reurn of 0.35%). REV herefore canno smulaneously explan he oppose paerns of he hgh reurns o pas ΔCVOL socks and he pas low reurns o pas ΔPVOL socks. When we compue alphas wh respec o he fve-facor model whch ncludes a shor-erm reversal facor we fnd he dfference n alphas beween he frs and enh ΔPVOL porfolos s 1.05% per monh wh a - sasc of In he nerne appendx we furher examne he predcably of mpled volaly nnovaons n dfferen sze lqudy and prce buckes. We fnd ha he predcably s sronges n he smalles socks bu he predcably of boh ΔCVOL and ΔPVOL s sll economcally large and hghly sascally sgnfcan among bg socks. The degree of ΔCVOL and ΔPVOL predcably s also smlar among relavely lqud versus relavely llqud socks and low-prced socks versus hgh prced socks. The reducon bu no elmnaon of he anomalous reurns n he larger and more lqud socks ndcaes ha here may be some lqudy frcons nvolved n mplemenng a radable sraegy based on ΔCVOL and ΔPVOL predcors. In he nerne appendx we presen furher resuls for oher screens relaed o lqudy and ransacons coss such as excludng he smalles leas-lqud and lowes-prced socks n he formaon of our porfolos. In all hese cases here reman economcally and sascally sgnfcan nex-monh reurns from formng porfolos ranked on ΔCVOL and ΔPVOL Long-Term Predcably 14

18 We nvesgae he longer-erm predcve power of ΔCVOL and ΔPVOL over he nex sx monhs by consrucng porfolos wh overlappng holdng perods followng Jegadeesh and Tman (1993). In a gven monh he sraegy holds porfolos ha are seleced n he curren monh as well as n he prevous K 1 monhs where K s he holdng perod (K = 1 o 6 monhs). A he begnnng of each monh we perform dependen sors on ΔCVOL conrollng for ΔPVOL over he pas monh. Based on hese rankngs 10 porfolos are formed for ΔCVOL. In each monh he sraegy buys socks n he Hgh ΔCVOL decle and sells socks n he Low ΔCVOL decle holdng hs poson for K monhs. In addon he sraegy closes ou he poson naed n monh K. Hence under hs radng sraegy we revse he weghs on 1/K of he socks n he enre porfolo n any gven monh and carry over he res from he prevous monh. Decle porfolos of ΔPVOL are formed smlarly. The profs of he above sraeges are calculaed for a seres of porfolos ha are rebalanced monhly o manan equal weghs. We repor he long-erm predcably resuls n Table 5. The average raw and rsk-adjused reurn dfferences beween Hgh ΔCVOL and Low ΔCVOL porfolos are sascally sgnfcan for oneo sx-monh holdng perods. There s a pronounced drop n he magnude of he average holdng reurn whch s reduced by more han a half beween monhs 1 and 2 from 1.38% per monh o 0.63% per monh respecvely. There s a furher reducon o 0.34% per monh afer four monhs. There are smlar reducons n he alphas across horzons. Clearly he predcably of ΔCVOL s no jus a one-monh affar bu s concenraed whn he nex hree monhs. The predcably of ΔPVOL also persss beyond one monh. The average reurn dfference beween he exreme ΔPVOL decle porfolos conrollng for ΔCVOL s 1.04% per monh a he one-monh horzon and lke he long-horzon reurn predcably paern for he ΔCVOL porfolos he predcably decreases by approxmaely half o 0.47% per monh a he wo-monh horzon. Afer hree monhs he economc and sascal sgnfcance of ΔPVOL porfolos dsappear. In summary ΔCVOL and ΔPVOL predcably persss for a leas hree monhs even longer n he case of ΔCVOL bu he srengh of he predcably s reduced by half afer one monh n boh cases Response of Opon Markes The porfolo level analyses n Tables 2-5 shows he sock marke reacs o opon marke nformaon. As Table 3 shows he large changes n opon prces occur conemporaneously wh opon volume. Is all hs nformaon mpounded n opon prces oday? We hank a referee for suggesng hs analyss. 15

19 We nvesgae hs ssue by lookng a he paern of mpled volales n he pre- and posformaon monhs. Takng he dependen 1010 sors consruced n Table 3 we compue he call and pu mpled volales from monh 6 o monh +6. In Fgure 1 Panel A we plo he level of call mpled volales for he Low ΔCVOL and Hgh ΔCVOL decles from he dependen sors of ΔCVOL conrollng for ΔPVOL porfolos formed a me from monh 6 o monh +6. For he Low ΔCVOL decle call mpled volales decrease from 66% o 56% from monh 2 o monh bu hen hey ncrease o 58% n monh +1 and reman a abou he same level over he nex sx monhs. Smlarly for he Hgh ΔCVOL decle call mpled volales frs ncrease from 55% o 66% from monh 2 o monh bu hen hey decrease o 59% n monh +1 and reman around here over he nex sx monhs. Thus afer call opon volales ncrease pror o me sock prces respond afer me bu here s lle response of opon markes afer he nal ncrease n ΔCVOL. Panel B of Fgure 1 repeas he same exercse for he Low ΔPVOL and Hgh ΔPVOL decles and also shows ha here s no movemen n pu mpled volales n he pos-formaon monhs. Ths s also conssen wh he nerpreaon ha nformed raders move opon prces oday and here s lle furher adjusmen on average n opon markes whle equy reurns adjus over he nex few monhs. Whle Fgure 1 examnes only he pre- and pos-formaon movemens n opon markes we show below ha conssen wh he model n he appendx nformed raders conemporaneously move boh sock and opon markes n he pre-formaon perod. Today s nformaon n opon volales however predcs sock reurns for several monhs aferwards. 4. Cross-Seconal Regressons wh ΔCVOL and ΔPVOL Whle Table 4 showed ha s unlkely mos frm characerscs and skewness measures play a role n he predcably of he cross secon of sock reurns by CVOL and PVOL dd no conrol smulaneously for mulple sources of rsk. We nvesgae hs now usng Fama and MacBeh (1973) regressons of sock reurns ono mpled volaly changes wh oher varables. Specfcally we run he followng cross-seconal regresson: R CVOL PVOL X (3) where R 1 s he realzed reurn on sock n monh +1 and X s a collecon of sock-specfc conrol varables observable a me for sock whch ncludes nformaon from he cross secon of socks and he cross secon of opons. We esmae he regresson n equaon (3) across socks a me and hen repor he cross-seconal coeffcens averaged across he sample. The cross-seconal regressons are run 16

20 a he monhly frequency from March 1996 o December To compue sandard errors we ake no accoun poenal auocorrelaon and heeroscedascy n he cross-seconal coeffcens and compue Newey-Wes (1987) -sascs on he me seres of slope coeffcens. The Newey-Wes sandard errors are compued wh sx lags Coeffcens on ΔCVOL and ΔPVOL Table 6 Panel A presens frm-level cross-seconal regressons wh call and pu mpled volaly nnovaons frs nroduced ndvdually and hen smulaneously ogeher wh conrols for frm characerscs and rsk facors. 12 We also nclude ΔCVOL and ΔPVOL smulaneously n mulvarae regressons wh conrol varables o deermne her jon effecs on sock reurns. In he presence of rsk loadngs and frm characerscs Regresson (1) n Panel A of Table 6 shows ha he average slope coeffcen on ΔCVOL s 1.57 whch s hghly sgnfcan wh a -sasc of In regresson (2) he average slope on ΔPVOL s 1.85 wh a -sasc Regresson (3) ncludes boh ΔCVOL and ΔPVOL wh coeffcens of 3.78 and 3.92 wh -sascs of 7.09 and 7.13 respecvely. These regressons confrm he robusness of ΔCVOL and ΔPVOL o predc fuure sock reurns as repored n Tables 2-5 excep he regressons conrol for a comprehensve se of frm characerscs rsk and skewness arbues. To provde an economc sgnfcance of he average slope coeffcens n Table 6 on ΔCVOL and ΔPVOL we consruc he emprcal cross-seconal dsrbuon of mpled volaly nnovaons over he full sample (summarzed n Table 1). The dfference n ΔCVOL (ΔPVOL) values beween average socks n he frs and enh decles s 22.4% (19.4%) for call (pu) mpled volaly nnovaons. If a frm were o move from he frs decle o he enh decle of mpled volales whle s oher characerscs were held consan wha would be he change n ha frm s expeced reurn? The ΔCVOL coeffcen of 3.78 n Table 6 Panel A represens an economcally sgnfcan effec of an ncrease of % 0.85% per monh n he average frm s expeced reurn for a frm movng from he frs o he enh decle of mpled volales and he ΔPVOL coeffcen of 3.92 represens a smlar decrease of % 0.76% per monh. These are smaller bu smlar o he 1.38% and 1.04% dfferences n he frs and enh decles n Table 4 for ΔCVOL and ΔPVOL respecvely because we conrol for he effecs of all oher frm characerscs rsk facors and loadngs. 12 To address poenal concerns abou ouler observaons we elmnae he 1s and 99h percenles of ΔCVOL and ΔPVOL and replcae Table 6. For furher robusness check n addon o excludng he 1s and 99h percenles of ΔCVOL and ΔPVOL we elmnae low-prced socks (prce < $5 per share). As shown n he nerne appendx he average slope coeffcens on ΔCVOL (ΔPVOL) reman posve (negave) and hghly sgnfcan afer elmnang he low-prced socks as well as he exreme observaons for call and pu mpled volales. 17

21 4.2. Oher Cross-Seconal Predcors In Panel A of Table 6 he sgns of he esmaed Fama-MacBeh coeffcens on he sock characerscs are conssen wh earler sudes bu some of he relaons are generally no sgnfcan. The log marke capalzaon (SIZE) and llqudy (ILLIQ) coeffcens are boh nsgnfcanly dfferen from zero. The momenum (MOM) effec s weak as well. Ths s because we use oponable socks ha are generally large and lqud where he sze and lqudy effecs are weaker (see for example Hong Lm and Sen 2000). We do observe a sgnfcan book-o-marke effec (see Fama and French ( )) and a sgnfcan reversal effec (see Jegadeesh (1990) and Lehmann (1990)). The mos neresng predcors for our purposes however are he ones ha are relaed o volaly and he opon marke. In regressons (1)-(3) he coeffcen on hsorcal volaly RVOL s negave bu sascally nsgnfcan. 13 Panel B of Table 1 repors ha RVOL has very low correlaons of 0.02 and 0.03 wh ΔCVOL and ΔPVOL respecvely. Ths ndcaes ha he effec of pas volaly s very dfferen from our cross-seconal predcably of ΔCVOL and ΔPVOL. In regresson (4) we drop RVOL and replace by he RVOL IVOL spread. We do no nclude RVOL and RVOL IVOL n he same regresson because hey are hghly correlaed. The ΔCVOL and ΔPVOL coeffcens are smlar across regressons (3) and (4). Pan and Poeshman (2006) fnd ha socks wh hgh C/P Volume ouperform socks wh low call-pu volume raos by more han 40 bass pons on he nex day and more han 1% over he nex week. However our resuls n Table 6 provde no evdence for a sgnfcan lnk beween C/P Volume and he cross-secon of expeced reurns. Ths s conssen wh Pan and Poeshman who show ha publcly avalable opon volume nformaon conans lle predcve power whereas her propreary measure of opon volume emanang from prvae nformaon does predc fuure sock reurns. As an alernave o opon radng volume we also examne C/P OI. Ths varable s hghly nsgnfcan as well. There are sronger effecs from alernave measures of mpled volaly spreads. In regresson (4) RVOL IVOL carres a negave and sascally sgnfcan coeffcen conssen wh Bal and Hovakman (2009). In regressons (1)-(4) he coeffcens on rsk-neural skewness QSKEW are negave and hghly sgnfcan as well. Ths s smlar o he paern of QSKEW wh he ΔCVOL and ΔPVOL average reurn paerns n Table 4 and also confrms he negave predcve relaon beween opon skew and fuure sock reurns n Xng Zhang and Zhao (2010). The hghly sascally sgnfcan loadngs on ΔCVOL and ΔPVOL n he presence of he negave QSKEW and RVOL IVOL coeffcens 13 Ths s smlar o he cross-seconal volaly effec of Ang e al. ( ) where socks wh hgh pas volaly have low reurns excep Ang e al. work manly wh dosyncrac volaly defned relave o he Fama and French (1993) model nsead of oal volaly. 18

22 mply ha he nformaon n opon volaly nnovaons s dfferen o he predcve ably of he opon skew and he varance rsk premum uncovered by prevous auhors. Cremers and Wenbaum (2010) nvesgae how he call-pu volaly spread whch s he dfference beween CVOL and PVOL predcs sock reurns and hey also repor he relaon beween ΔCVOL ΔPVOL and sock reurns n passng. 14 They do no focus on unvarae predcably of ΔCVOL or ΔPVOL or unconsraned jon predcably of hese varables. 15 Cremers and Wenbaum pon ou ha he srengh of predcably from call-pu volaly spreads declnes durng her sample perod becomng nsgnfcan over he second half of her sample In he nerne appendx we show ha he predcably from usng ΔCVOL and ΔPVOL s robus o dfferen sample perods. Specfcally he full sample s frs dvded no wo subsample perods (January 1996 December 2003 and January 2004 December 2011) and hen for addonal robusness s dvded no hree subsample perods (January 1996 December 2000 January 2001 December 2005 and January 2006 December 2011). Afer conrollng for frm characerscs rsk and skewness arbues he average slope coeffcens on ΔCVOL (ΔPVOL) are posve (negave) and hghly sgnfcan for all subsample perods ncludng Informed Tradng The model of nformed radng n Appendx A makes hree predcons assocaed wh he predcably of pas changes n opon volales for sock reurns. Frs he predcably should be greaer (1) when pas opon volales have ncreased conemporaneously wh sock prces (2) when large changes n opon volales are accompaned by unusually large radng volume n opon markes and (3) should be especally srong when here s large radng volume n boh opon and sock markes. Ineracons wh Pas Sock Reurns 14 The nerne appendx also shows ha conrollng for he Cremers and Wenbaum (2010) varable CVOL PVOL n he regressons does no affec our man fndngs. We fnd ha he coeffcen on CVOL PVOL s posve and sascally sgnfcan conssen wh Cremers and Wenbaum bu he coeffcens on ΔCVOL and ΔPVOL are smlar o hose repored n Table 6 and are hghly sascally sgnfcan. 15 We rejec he null hypohess ha he average slope coeffcens on he changes n call and pu mpled volales are dencal wh a -sasc of 2.17 (p-value = 3%). Ths mples ha ΔCVOL and ΔPVOL have sgnfcan and dfferen mpacs on fuure sock reurns rejecng he consraned jon predcably of hese varables. 16 In he nerne appendx we also presen resuls from he pooled panel regressons for he full sample perod. The sandard errors of he parameer esmaes are clusered by frm and me. The pooled panel regresson resuls ndcae ha afer conrollng for all frm characerscs rsk and skewness arbues he slope coeffcens on ΔCVOL (ΔPVOL) are posve (negave) and hghly sgnfcan smlar o our fndngs from he Fama-MacBeh regressons repored n Table 6 Panel A. 19

23 An nformed nvesor can rade boh sock and opon markes so nuvely boh markes should respond conemporaneously. 17 The predcably by pas CVOL for fuure sock reurns should be especally srong when sock markes have also moved wh CVOL. In regressons (5)-(8) of Panel A Table 6 we es wheher here s greaer predcably by CVOL and PVOL when pas ncreases n opon volales are accompaned by conemporaneous ncreases n sock reurns. We creae a varable PasReDecle whch akes values from 1 o 10 for socks ranked no decles based on her pas one-monh reurns (REV). We nerac hs wh he CVOL and PVOL varables. A posve coeffcen on he neracon erm s evdence conssen wh nformed radng akng place n boh opon and sock markes. We fnd hs s ndeed he case. In each regresson (5)-(8) he average slope coeffcens on he CVOL PasReDecle neracon erms are posve wh -sascs above 2.2. Thus CVOL predcably s sronges n socks ha have conemporaneously experenced ncreases n prce over he prevous perod. Ths reflecs ha nformed nvesors can also rade socks or he call opon prces feedback ono sock prces or boh. The coeffcens on PVOL PasReDecle are also posve bu he ndvdual coeffcens on PVOL and REV are hemselves negave. Hence he posve coeffcen on PVOL PasReDecle s also conssen wh he model s predcon ha when nvesors demand of boh socks and opons s hgh he cross-marke predcably of opons o socks s enhanced. Opon Volume We conduc a furher nvesgaon of nformed radng n Panel B of Table 6 by focusng on where radng akes place. We run cross-seconal regressons wh he followng regressors: 18 HghCallVol CVOL = CVOL f Call Volume Medan (4) 0 oherwse LowCallVol CVOL = CVOL f Call Volume Medan 0 oherwse 17 The demand-based opon prcng models of Bollen and Whaley (2004) and Garleanu Pedersen and Poeshman (2009) do no drecly predc ha here should be lead-lag relaons beween opon and sock markes. In addon o a demand effec n opon markes here mus be a non-nsananeous response of he underlyng sock marke. Some raonal and behavoral models explan hs delayed reacon ncludng nformaon mmobly (Van Neuwerburgh and Veldkamp 2009) lmed aenon (Hrshlefer 2001) bounded raonaly or lmed updang of belefs of agens n he sock marke (Sargen 1994) or he slow dssemnaon of news or nal lmed access o ha news (see e.g. Hong and Sen 1999). Our model n Appendx A shows ha he acon of nformed raders can produce jon opon marke o sock marke predcably and vce versa n a nosy raonal expecaons model. 18 A smlar economerc specfcaon s proposed by Bal (2000) o es he presence and sgnfcance of asymmery n he condonal mean and condonal volaly of neres rae changes. 20