The Joint Cross Section of Stocks and Options *

Transcription

1 The Jon Cross Secon of Socks and Opons * Andrew Ang Columba Unversy and NBER Turan G. Bal Baruch College, CUNY Nusre Cakc Fordham Unversy Ths Verson: 1 March 2010 Keywords: mpled volaly, rsk premums, reurn predcably, momenum JEL Classfcaon: G10, G11, C13. * We hank Larry Glosen, Bob Hodrck, and Yuhang Xng for helpful commens. Columba Busness School, 3022 Broadway, 413 Urs, New York, NY Phone: (212) , Emal: [email protected]. Deparmen of Economcs and Fnance, Zckln School of Busness, Baruch College, One Bernard Baruch Way, Box , New York, NY Phone: (646) , Emal: [email protected]. School of Busness, Fordham Unversy, 1790 Broadway, New York, NY 10019, Phone: (212) , Emal: [email protected].

2 The Jon Cross Secon of Socks and Opons ABSTRACT Opon volales have sgnfcan predcve power for he cross secon of sock reurns and vce versa. Socks wh large ncreases n call mpled volales end o rse over he followng monh whereas ncreases n pu mpled volales forecas fuure decreases n nex-monh sock reurns. The spread n average reurns and alphas beween he frs and ffh qunle porfolos formed by rankng on lagged changes n mpled call volales s approxmaely 1% per monh. Gong n he oher drecon, socks wh hgh reurns over he pas monh end o have call opon conracs ha exhb ncreases n mpled volaly over he nex monh, bu realzed volaly ends o decrease. The resuls are conssen wh he slow dffuson of nformaon across opon and underlyng equy markes and are suggesve of nformed radng occurrng n boh asse markes.

3 1. Inroducon Opons are redundan asses only n a world of complee and compeve markes wh no ransacons coss, symmerc nformaon, and no resrcons on shorng. No surprsngly, snce n he real world none of hese assumpons hold, opons are no spanned by sock prces and opon prces are no merely funcons of underlyng sock prces and rsk-free secures. Many heorecal models jonly prcng opons and underlyng asse prces n ncomplee markes have ncorporaed many of hese real-world frcons, such as Deemple and Selden (1991), Back (1993), Cao (1999), Burasch and Jlsov (2006), and Vanden (2008), among ohers. In addon, f nformed raders end o choose ceran markes over ohers, nformaon-based models such as Easley, O Hara and Srnvas (1998) predc ha hose markes where nformed radng akes place wll lead oher markes where nformed radng does no predomnae. Opon markes have sgnfcan advanages for nformed raders, whch are enumeraed by Black (1975), Grossman (1977), Damond and Verrecha (1987), and ohers. Opons offer an alernave way o ake shor posons when shor posons n he underlyng asse would be prohbvely expensve. Opons provde addonal leverage whch may no be possble o oban n sock and bond markes (see Back, 1993; Bas and Hllon, 1994). Opons also reduce ransacons coss of makng replcang rades n he underlyng socks. On he oher hand, s no obvous ha an nformed rader would frs choose opons markes over underlyng equy markes. As Easley, O Hara and Srnvas (1998) show, only when he mplc leverage avalable n opons s large and he opon marke offers suffcen lqudy wll nformed nvesors frs rade n opon markes. Conversely, f nformed raders can more easly hde n equy markes, hen equy reurns wll lead opon prces. In hs paper we documen ha he cross secon of opon volales conans nformaon ha forecass he cross secon of expeced sock reurns. We fnd ha news arrvals, as measured by opon volaly nnovaons, sgnfcanly predc he cross secon of sock reurns. Pus and calls conan dfferen nformaon. Socks wh call opons whch have experenced large ncreases n volales over he pas monh end o experence hgh expeced reurns over he nex monh whle large ncreases n pu opon volales predc decreases n fuure sock reurns. We also uncover evdence of reverse dreconal predcably ha pas sock reurns cross-seconally predc opon mpled volales. Socks wh hgh pas reurns over he prevous monh end o have call opons whch exhb ncreases n volaly over he nex monh. Our resuls are remarkable for several reasons. Frs, he predcably of sock reurns and opon mpled volales we documen s a he sandard monhly horzon used by many sudes examnng cross-seconal sock reurn predcably. Mos of he leraure examnng lead-lag effecs of opons 1

4 versus sock markes, whch ncludes Manaser and Rendleman (1982), Bhaacharya (1987), Kumar, Sarn and Shasr (1992), and Sephan and Whaley (1990), among many ohers, have examned nra-day or daly frequences. The monhly frequency suggess he predcably s unlkely due o mcrosrucure radng effecs of asymmerc nformaon rades. Second, our preferred measures of news arrvals n opon and sock markes are very smple: he frs dfference n opon volales over he pas monh or he sock reurn, relave o a facor model, over he prevous monh. We also consder more sophscaed measures of opon mpled volaly nformaon ha ake advanage of nformaon n he me seres of opon prces and cross-seconal sock and opon nformaon. These measures produce very smlar resuls. Some recen sudes ncludng Bal and Hovakman (2009), Cremers and Wenbaum (2009), and Xng, Zhang, and Zhao (2009) documen ha varous sascs compued from opon volales predc underlyng sock reurns. These nclude measures of he dfference beween mpled and realzed volales, pu-call pary devaons, and measures of rsk-neural skewness. Cremers and Wenbaum (2009) show ha pu-call pary devaons can predc sock reurns only a very shor horzons and he effec has become much weaker n more recen daa. The opon volaly nnovaon measure we use s a very smple measure of news nformaon n opon marke and s very dfferen o mpled mnus realzed volales and rskneural skewness measures. Smlarly, here are some recen sudes documenng ha he cross secon of opons s predcable by varous nsrumens. For example, Goyal and Sareo (2009) show ha dela-hedged opons wh a large posve dfference beween hsorcal, or realzed, volaly and mpled volaly have low average reurns. They also fnd ha several sandard sock characerscs also have predcve power for he cross secon of opon reurns. Roll, Schwarz and Subrahmanyam (2009) examne he conemporaneous, bu no predcve, relaon beween opons radng acvy and sock reurns. To our knowledge we are he frs o documen ha smple lagged sock reurns cross-seconally predc opon volales. Call opon volales ncrease, on average, over he nex monh for socks whch have experenced hgh reurns over he pas monh. The call volales also end o ncrease more han pu volales. Surprsngly, fuure realzed volales end o move n he oppose drecon and decrease whle mpled volales end o ncrease. Covarances wh sock characerscs and opon nsrumens, lke he dfference beween realzed and mpled volales, are no hgh enough o explan he predcve role of pas sock reurns on he cross secon of opon mpled volales. Thrd, our resuls are very robus. Naurally, hey are robus o he usual cross-seconal rsk facor and characersc conrols usng boh sock and opon nformaon. The predcably of sock reurns by opon nnovaons s also robus n several subsamples. Whereas many cross-seconal 2

5 sraeges have reversed sgn or become much weaker durng he recen fnancal crss, he ably of opon volales o predc reurns s sll seen n very recen daa. In parcular, he predcve relaon beween large pu volaly nnovaons and fuure low sock reurns s very promnen n In addon, we fnd ha he economc source of he reurn predcably by opon nnovaons s almos all due o changes n dosyncrac, no sysemac, componens of mpled volales. Fnally, he predcably we documen s sascally very srong and economcally large. Qunle 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. The dfference beween he op and boom qunle porfolos n rankng socks by pas changes n pu mpled volales s approxmaely 60 bass pons per monh afer conrollng for he effec of call volaly nnovaons. In he oher drecon, socks wh abnormal reurns of 1% relave o he CAPM end o see call volales ncrease over he nex monh by approxmaely 3%. Our emprcal fndngs are conssen wh models where nformaon slowly dffuses across opon and underlyng equy markes and are suggesve of boh nformed radng mpacng opon and sock markes. In parcular, our resuls are parally conssen wh boh demand-based opon prcng models where margnal end users of dervaves place nformed opon rades. They may also be explaned by behavoral under-reacon models where opons and underlyng sock markes have dfferen ypes of agens who do no opmally ake advanage of all prce sgnals and nformaon. Imporanly, he cross-predcably of socks o opons and vce versa ndcaes ha prce dscovery akes place n boh asse markes. The res of hs paper s organzed as follows. In Secon 2 we descrbe he daa and descrbe he varous measures of nnovaons n opon volales. Secons 3 and 4 presen he man emprcal resuls on he cross-seconal predcably of sock reurns by opon mpled volaes. We consder crossseconal regressons predcng fuure sock reurns wh opon volaly nnovaons n Secon 3 and consruc porfolos ranked on pas call and pu volaly nnovaons n Secon 4. Secon 5 presens resuls from predcng he cross secon of mpled volaly nnovaons usng he cross secon of sock reurns. Secon 6 nerpres our resuls n an economc conex and Secon 7 conans some concludng remarks. 3

6 2. Daa and Volaly Innovaons We descrbe he mpled volaly daa n Secon 2.1 and he oher facor rsk loadngs and characerscs n Secon 2.2. We nroduce several measures of opon volaly nnovaons rangng from smple frs dfferences o me-seres and cross-seconal esmaes n Secon 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 dae o accuraely compue an nerpolaed value. The nerpolaons are done each day so ha no forward-lookng 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 a-he-money call and pu opons mpled volales wh a dela of 0.5 and an expraon of 30 days. Some robusness ess wll also nvesgae an expraon of 91 days. We use he longes sample avalable from January 1996 o Sepember Panel A of Table 1 repors he average number of socks per monh for each year from 1996 o There are 1292 socks per monh n 1996 rsng o 2175 socks per monh n We repor he average and sandard devaon of he end-of-monh annualzed call and pu mpled volales of a-hemoney, 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 recen fnance crss n 2008, we observe a sgnfcan ncrease n average mpled volales from around 40% o 54% for boh CVOL and PVOL. 1 1 There are many reasons why Black-Scholes (1973) and pu-call pary do no hold, as documened by Ofek, Rchardson and Whelaw (2004) and Cremers and Wenbaum (2009), among ohers. The 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 bdask spreads and non-synchronous rades. These mcrosrucure ssues do no affec he use of our opon volales as predcve nsrumens observable a he begnnng of each perod. 4

7 2.2. Facor Loadngs and Sock Characerscs 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 ha are wdely known n he leraure o be assocaed wh expeced sock reurns: BETA: To esmae he monhly bea of an ndvdual sock we esmae marke model regressons a a daly frequency: R d rf, d = α + β( Rm, d rf, d ) + ε 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 m,d o be he CRSP daly value-weghed ndex and r f,d o be he Ibboson rskfree rae. We esmae equaon (1) for each sock usng daly reurns whn a monh. The esmaed slope coeffcen ˆβ s he marke bea of sock n monh. SIZE: Followng he exsng leraure, frm sze s measured by he naural logarhm of he marke value of equy (a sock s prce mes shares ousandng n mllons of dollars) a he end of 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 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. 5

8 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 =, where R s he reurn on sock n monh, and VOLD s he respecve monhly radng volume n dollars. 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 whn monh,.e. RVOL = var( R d ). We denoe he monhly frs dfferences n RVOL as ΔRVOL. Call/Pu (C/P) volume: Followng Pan and Poeshman (2006), we use he rao of call/pu opon radng volume over he prevous monh as a poenal deermnan of fuure sock reurns. Call/Pu open neres (C/P OI): As an addonal conrol varable we use he rao of call/pu open neres whch may poenally predc fuure sock reurns. Realzed-Impled volaly spread (RV-IV): Followng Bal and Hovakman (2009) and Goyal and Sareo (2009), we conrol for he dfference beween he monhly realzed volaly and he average of he a-he-money call and pu mpled volales (usng he Volaly Surface sandardzed opons wh a dela of 0.50 and maury of 30 days). Rsk-neural measure of skewness (QSKEW): Followng Conrad, Dmar and Ghysels (2009) and Xng, Zhang and Zhao (2009), we conrol for he rsk-neural measure of 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-hemoney call and pu mpled volales (wh delas of 0.50), boh usng maures of 30 days Measures of Volaly Innovaons Frs Dfferences of Impled Volaly Levels The frs, and smples, defnon of volaly nnovaons s he change n call and pu mpled volales, whch we denoe as ΔCVOL and ΔPVOL, respecvely. As an addonal robusness check, 6

9 we also consder proporonal changes n CVOL and PVOL defned as % ΔCVOL % ΔPVOL = = ( CVOL CVOL 1 ) CVOL 1, ( PVOL PVOL ) PVOL. 1 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 and cross secon. Our wo oher measures accoun for hese dmensons of predcably. Tme-Seres Innovaons Impled volales are well known o be perssen. To ake accoun of hs me-seres predcably we assume an AR(1) model for mpled volales and esmae he followng regresson usng he pas wo years of monhly daa: CVOL = a + b CVOL + ε, c c c 1 PVOL = a + b PVOL + ε. p p p 1 (3) We defne he curren n call and pu mpled volales for sock n monh as he c monhly nnovaons n call and pu mpled volales. Tha s, we assgn he me value of ε and as he opon nnovaons and denoe hem as s CVOL and PVOL s p ε, respecvely, wh he s subscrp denong ha hey are nnovaons derved from me-seres esmaors. Noe ha he ΔCVOL and ΔPVOL frs dfference measures mplcly assume ha b = b = 1. c p Cross-Seconal Innovaons We can alernavely esmae monhly nnovaons n volales by explong he cross-seconal predcably of mpled volales. We denoe he cross-seconal nnovaons as CVOL cs and PVOL cs, wh he cs subscrp denong hey are cross-seconal esmaors of mpled volaly nnovaons, and esmae hem usng frm-level cross-seconal regressons for each monh : CVOL PVOL = a = a c p + b c + b p CVOL PVOL ε c p + ε, (4) 7

10 where he cross secon of call and pu mpled volales are regressed on her one-monh lagged values c p for each monh. The resduals of hese cross-seconal regressons a me, ε and ε, are used as measures of volaly nnovaons, denoed by CVOL cs and PVOL cs, respecvely. 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 where when curren sock volaly ncreases, all opon conracs across all srkes and maures reflec hs general ncrease of volaly. Boh CVOL and PVOL have a correlaon of 67% wh pas realzed volaly whch reflecs he perssence of volaly. The frs dfferences n mpled volales, ΔCVOL and ΔPVOL, are less correlaed, a 57%, han he levels CVOL and PVOL, whch have a correlaon of 92%. Ths lower correlaon mples ha he cross secon of pu volaly nnovaons may conan dfferen nformaon from he cross secon of call volaly nnovaons, whch we confrm below, bu neverheless ndcaes ha here s a srong common componen n boh call and pu volaly nnovaons. The changes n mpled volales are no correlaed wh eher RVOL or ΔRVOL, wh correlaons of ΔCVOL wh RVOL and ΔRVOL beng 0.04 and 0.10, respecvely. The correlaons of ΔPVOL wh RVOL and ΔRVOL are also low a 0.05 and 0.11, 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. The me-seres and cross-seconal nnovaons of CVOL and PVOL are smlar o he frsdfference esmaes. Ths s seen n he hgh correlaons of ΔCVOL wh ΔCVOL wh CVOL s, a 0.83, and of CVOL cs, a Smlarly ΔPVOL has correlaons of 0.81 and 0.95 wh PVOL s and PVOL cs, respecvely. Thus, he nformaon n all hree measures of mpled volaly nnovaons s smlar and we expec ha all he nnovaon measures may have roughly he same degree of predcve ably. 8

11 3. Predcng he Cross Secon of Sock Reurns wh Impled Volales In hs secon we nvesgae he cross-seconal relaon beween mpled volaly s and expeced sock reurns a he frm level usng cross-seconal regressons. These regressons ake he form: R,, + 1 λ0 λ1 X, ε, + 1 = + + (5) where R 1 s he realzed reurn on sock n monh +1 and X, s a collecon of sock-specfc, + varables observable a me for sock whch ncludes nformaon from he cross secon of socks and he cross secon of opons. Followng Fama and MacBeh (1973), we esmae he regresson n equaon (5) across socks a me and hen repor he cross-seconal coeffcens λ 1 averaged across he sample. The cross-seconal regressons are run a he monhly frequency over 152 monhs from February 1996 o Sepember 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. We frs examne he effec of unexpeced changes of mpled volales on he cross secon of sock reurns usng frs-dfference nnovaons of mpled volales n Secon 3.1. We fnd srong evdence ha ncreases n call volaly and decreases n pu volaly forecas hgh fuure sock reurns n he cross secon. We examne he effec usng alernave measures of volaly nnovaons and a range of conrol varables n Secon 3.2. In Secon 3.3 we exend our analyss o me-seres and crossseconal esmaors of opon volaly nnovaons. We examne wheher he sgnfcanly posve (negave) relaon beween expeced reurns and he call (pu) mpled volaly changes s drven by he sysemac and/or dosyncrac componens n Secon Frs-Dfference Innovaons of Impled Volales In Table 2 we repor cross-seconal coeffcens of varous mpled volaly measures. Regressons (1) and (2) use he level of opon mpled volales CVOL and PVOL, respecvely, whle regresson (3) ses RVOL as he regressor. We repor Newey-Wes (1987) adjused -sascs n parenheses. In regressons (1)-(3) all he coeffcens are negave and sascally nsgnfcan. The negave coeffcen on he realzed or opon volales s conssen wh he well-known leverage effec operang a he ndvdual sock level (see, among many ohers, Bekaer and Wu, 2000; Fglewsk and Wang, 2000) where hgh volales forecas low sock reurns. From hese resuls we canno rejec he hypohess ha 9

12 here s no lnk beween he level of mpled and realzed volales and he cross secon of expeced reurns. In regressons (4)-(6) we use frs-dfference nnovaons of mpled and realzed volales o predc he cross secon of sock reurns. Regresson (4) repors ha he slope on ΔCVOL s 1.87 wh a - sasc of The coeffcen on ΔPVOL s 0.95 wh a -sasc of 2.09 n regresson (5). In conras, here s no predcve power of changes n RVOL n regresson (6), whch has a coeffcen close o zero wh a -sasc of Thus, unexpeced news n mpled volales, bu no pas volales, cross-seconally predc sock reurns. Unexpecedly hgh call volales forecas ncreases n fuure sock reurns whle unexpecedly hgh pu volales predc declnes n fuure sock reurns. Regressons (7) and (8) repor ha hese resuls are robus o measurng nnovaons n percenage erms raher han jus usng level dfferences. In percen changes he resuls have even hgher sascal sgnfcance. The coeffcen on %ΔCVOL s 1.11 wh a -sasc of 3.63 and he slope on %ΔPVOL s 0.70 wh a -sasc of 3.27, compared o -sascs of 2.90 and 2.09 correspondng o he coeffcens on ΔCVOL and ΔPVOL n regressons (4) and (5), respecvely. Regresson (9) agan shows ha nnovaons n realzed volaly measured n percenage erms have no ably o cross-seconally predc sock reurns. The unvarae regressons show ha here s srong evdence ha changes n call and pu mpled volales affec sock reurns. We nex ask f he predcably exends o mulvarae specfcaons. In regressons (10) and (11) we use boh changes n call and pu mpled volales n bvarae crossseconal regressons. 2 Table 2 shows ha he average slopes on ΔCVOL and %ΔCVOL are posve and hghly sgnfcan wh -sascs of 5.02 and 5.76, respecvely. Smlar o our earler fndngs wh changes n pu volales n unvarae regressons, he average slopes on ΔPVOL and %ΔPVOL are negave wh coeffcens of 2.86 and 1.68, respecvely. These coeffcens are also hghly sgnfcan wh -sascs of 5.32 and 6.84, respecvely. The sascal sgnfcance of hese coeffcens s much sronger when ncludng changes n boh call and pu volales jonly n he cross-seconal regressons (10) and (11) compared o he unvarae regressons (4)-(5) and (7)-(8). Ths s no due o collneary; Table 1 makes clear ha he correlaon beween ΔCVOL and ΔPVOL s 0.57 and so changes n call and pu volales capure dfferen nformaon. The sronger sascal sgnfcance s due o explong hs nformaon jonly n one regresson and conrollng smulaneously for each effec. We also explore he jon nformaon n pu and call opon changes n Secon 5 below by consrucng porfolo reurns ranked on boh call and pu volaly nnovaons. 2 When ΔRVOL s ncluded as an addonal regressor he coeffcens on ΔCVOL and ΔPVOL are almos unchanged and he coeffcen on ΔRVOL s very close o zero and sascally nsgnfcan. 10

13 To check wheher our resuls are sensve o he sample perod we repor subsample analyss n Table 3 for he bvarae ΔCVOL and ΔPVOL cross-seconal regresson. We frs decompose he orgnal sample perod of January 1996 Sepember 2008 no wo subsamples: January 1996 o December 2001 and January 2002 o Sepember We repor he full sample coeffcens n he frs column, whch are dencal o regresson (10) n Table 2, for comparson. As shown n he second wo columns of Table 3, he average slopes on ΔCVOL (ΔPVOL) are posve (negave) and hghly sgnfcan for boh sample perods. The coeffcen on ΔCVOL s slghly lower, a 2.66, over he second subsample compared o a value of 3.60 over he whole sample, bu s sll sascally sgnfcan a he 99% level wh a Newey- Wes -sasc of In comparson he coeffcens on ΔPVOL are relavely unchanged across he whole sample a 2.86 and across each subsample, wh coeffcens of 2.43 and 2.98, respecvely. In he las column of Table 3, we nvesgae he predcve power of ΔCVOL and ΔPVOL durng he fnancal crss n Durng hs perod volales on all socks ncreased remendously. Table 3 repors ha he coeffcens on boh ΔCVOL and ΔPVOL reman posve and negave, respecvely, wh coeffcens of 3.48 and 4.06, respecvely. These are smlar o he full sample esmaes of 3.60 for ΔCVOL and 2.86 for ΔPVOL. Despe he very shor sample of only nne monhs, he coeffcen on ΔPVOL s even sascally sgnfcan wh a Newey-Wes -sasc of Clearly he recen fnancal crss has no dened he predcve ably of hese varables. Overall, hese resuls ndcae srong sgnfcance of he call and pu mpled volaly s as jon deermnans of he cross-secon of fuure reurns. Increases n call volales forecas ncreases n sock expeced reurns and ncreases n pu volales ac n he oppose drecon, forecasng decreases n fuure sock reurns Volaly Innovaons and Oher Cross-Seconal Predcors Table 4 presens frm-level cross-seconal regressons wh volaly nnovaons measured by frs dfferences from wo maures and oher conrol varables. The frs regresson n Table 4 repors he coeffcens on ΔCVOL and ΔPVOL n he same bvarae cross-seconal regresson specfcaon repored n regresson (10) from Table 2 for comparson whch uses an expraon of 30 calendar days. We also repea he analyss for opon volales for an expraon of 91 days n columns (4)-(6). Regresson (2) nroduces oher rsk loadngs and characerscs. In he presence of hese varables he coeffcen on ΔCVOL falls from 3.60 n he bvarae specfcaon (1) o 1.58 n regresson (2) bu s sll sgnfcan wh a -sasc of The coeffcen on ΔPVOL remans almos unchanged a 2.84 wh a -sasc of 4.46 compared o 2.86 n he frs column. Thus, he posve coeffcen on 11

14 ΔCVOL and he negave coeffcen on ΔPVOL are robus o he sandard cross-seconal predcors and have very srong sascal predcably n he presence of he sandard rsk varables. In Table 4 he sgns of he esmaed Fama-MacBeh coeffcens on he facors are conssen wh earler sudes, bu he relaons are generally no sascally sgnfcan. The log marke capalzaon (SIZE) and log book-o-marke rao (BM) coeffcens ndcae a small-large and a valuegrowh effec wh negave and posve coeffcens, respecvely, bu boh are nsgnfcanly dfferen from zero. The momenum (MOM) and shor-erm reversal (REV) effecs are also sascally weak. Ths s because we use oponable socks ha are generally large and lqud where he book-o-marke effec s weaker (see Loughran, 1997). Oponable socks are sgnfcanly dfferen from he usual CRSP unverse whch conans many more small, llqud, and low-prced socks wh srong reversal and momenum effecs (cf. Hong, Lm and Sen, 2000). In regresson (2) he coeffcen on hsorcal volaly, RVOL, s 1.14 and hghly sascally sgnfcan wh a -sasc of Ths s smlar o he cross-seconal volaly effec of Ang e al. (2006, 2009) 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. Panel B of Table 1 repors ha RVOL has very low correlaons of 0.04 and 0.05 wh ΔCVOL and ΔPVOL, respecvely. Ths ndcaes ha he effec of pas volaly s very dfferen from our crossseconal predcably of ΔCVOL and ΔPVOL. We use four addonal cross-seconal varables from opons n addon o ΔCVOL and ΔPVOL, whch are he log call-pu rao of opon radng volume (C/P Volume), he log rao of call-pu open neres (C/P OI), he realzed-mpled volaly spread (RV-IV), and he rsk-neural measure of skewness (QSKEW). The relaon beween opon volume and underlyng sock reurns has been exensvely suded n he leraure by Sefan 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. 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. Our resuls n Table 5 show ha here s a small posve relaon, less han 0.03, beween C/P Volume and he cross-secon of expeced reurns, bu C/P Volume s no sgnfcan n regressons (2) and (3). 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 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 wh a coeffcen close o zero. 12

15 Bal and Hovakman (2009) fnd ha socks wh low RV-IV spreads ouperform socks wh hgh RV-IV spread by 63 o 73 bass pons n he nex monh. In regresson (3) we nclude RV-IV bu drop he RVOL measure o avod collneary. The resuls n regresson (3) confrm he same drecon of a relaon beween a negave RV-IV spread and posve expeced reurns, bu he relaon s nsgnfcan a he 95% level. In he presence of RV-IV, he coeffcen on ΔCVOL decreases slghly o 1.26 compared o 3.60 n regresson (1) and 1.58 n regresson (2), bu s sll sgnfcan a he 95% level. In all hree regressons (1)-(3), he coeffcen on ΔPVOL remans remarkably unchanged close o 2.9 wh -sascs well below 4. The las varable n Table 4 s he measure of skewness from opon prces, QSKEW. Xng, Zhang and Zhao (2009) fnd ha socks whch exhb a pronounced degree of negave skewness n opon markes, measured by hgh ou-of-he-money pu mpled volaly compared o a-he-money call mpled volales, have low reurns. On he oher hand, Conrad, Dmar and Ghysels (2009) fnd he oppose relaon wh a more general measure of opon skewness derved from usng he enre cross secon of opons based on Baksh Kapada and Madan (2003). In regresson (2), he coeffcen on QSKEW s 3.40 and hs carres a hghly sgnfcan -sasc of Ths confrms he negave predcve relaon beween opon skew and fuure sock reurns n Xng, Zhang and Zhao (2009). The hghly sascally sgnfcan loadngs on ΔCVOL and ΔPVOL n he presence of he negave QSKEW coeffcen mply ha he nformaon n opon volaly nnovaons s dfferen from he prevously documened predcve ably of he opon skew for he cross secon of sock reurns. The second se of columns (4)-(6) n Table 4 repea he same exercse wh he Volaly Surface daa usng a maury of 91 days. For hs maury we fnd ha he coeffcens n he cross-seconal regresson conrollng for all rsk varables on ΔCVOL and ΔPVOL are larger n magnude and have hgher sascal sgnfcance han he 30-day maury coeffcens. Wh he 91-day maury he ΔCVOL and ΔPVOL coeffcens n regresson (5) are 4.37 and 4.73, wh -sascs of 5.70 and 5.79, respecvely, compared o 1.58 and 2.85 wh -sascs of 3.27 and 4.46 for he 30-day maury n regresson (2). Volumes for opons wh longer maures end o be lower as hese conracs end o be more llqud han he shores maury opon conracs so hese resuls should be nerpreed wh cauon. On he oher hand, he Volaly Surface daa uses all avalable opon nformaon across all srkes and maures n he nerpolaon of he 91-day maury. Table 4 shows ha he longer horzon allows for sronger predcably of he cross secon of socks, perhaps because longer-daed opons are more sensve o dreconal nformaon capured by ΔCVOL and ΔPVOL on he underlyng socks. 13

16 The clear concluson n Table 4 s ha cross-seconal regressons wh and whou rsk facors and characerscs provde srong evdence for a sgnfcanly posve (negave) relaon beween he changes n call (pu) opons mpled volales and fuure sock reurns Tme-Seres and Cross-Seconal Innovaons of Impled Volales In Table 5 we exend our analyss o he me-seres and cross-seconal measures of opon volaly nnovaons. The resuls n Table 5 echo he man conclusons n Table 4. Ths s perhaps no surprsng snce Table 1 shows he correlaons beween he me-seres nnovaons, he cross-seconal nnovaons, CVOL cs and CVOL s and PVOL s, and PVOL cs, wh he smple frs-dfference counerpars ΔCVOL and ΔPVOL are very hgh. Frs, he average slope coeffcens on he CVOL nnovaon measures are sgnfcanly posve. In he cross-seconal regresson (2) wh rsk conrols, he coeffcen on sasc of Smlarly, he coeffcen on he cross-seconal nnovaon, sasc of 3.14 conrollng for oher predcors n regresson (5). 3 nsead of RVOL, he coeffcens on CVOL s and CVOL s s 2.87 wh a - CVOL cs, s 1.72 wh a - In regressons (3) and (6) wh RV-IV CVOL cs are smlar. Second, pu volaly nnovaons agan ener wh a hghly sascally sgnfcan negave sgn. These coeffcens are larger n absolue value han he coeffcens on he call volaly nnovaons. The mpled pu volaly meseres (cross-seconal) nnovaon coeffcen n he regresson s 4.53 ( 3.46), wh a -sasc of 5.05 ( 5.26). Agan hese coeffcens are very smlar when RV-IV s ncluded as a conrol varable n regressons (3) and (6). Thrd, he predcve ably of he call and pu nnovaons esmaed from meseres and cross-seconal relaons s robus o conrollng for he sandard predcve characerscs such as SIZE, BM, MOM, and he opon predcve varables C/P Volume, C/P OI, RVOL or RV-IV, and QSKEW. Overall, our fndngs from he monhly changes and monhly me-seres and cross-seconal nnovaons ndcae ha unexpeced news or nformaon s o call and pu mpled volales are able o predc he cross-seconal varaon n sock reurns. 3 In unrepored resuls we commen ha predcve coeffcens are slghly larger n absolue value on he crossseconal s when we augmen he regresson n equaon (4) wh one-monh lagged realzed volales for each frm a me. 14

17 3.4. Sysemac vs. Idosyncrac Volaly Innovaons Impled call and pu volales conan boh sysemac and dosyncrac componens. In hs secon, we nvesgae f he predcve nformaon n mpled volaly nnovaons reflecs news arrvals n sysemac rsk, dosyncrac componens, or boh. Ths exercse sheds lgh on wheher he forecasng power of call and pu volaly nnovaons s comng from news n rsk premum componens, a leas measured by exposure o he marke facor, or by non-marke relaed volaly changes. We decompose he oal mpled varance no a sysemac componen and an dosyncrac componen usng a condonal CAPM relaon: 2 where σ s he rsk-neural varance of sock σ, = β, σm, + σ ε,,, (6) σ s he rsk-neural varance of he marke m, β s 2 m, 2 he marke bea of sock and σ s he dosyncrac rsk-neural varance of sock all a me. We ε,, follow Duan and We (2009) and esmae he bea from he rsk-neural, no he real, measure o oban esmaes of he sysemac and dosyncrac componens of mpled volales usng only opon daa. Ths s done by nferrng he sock bea from he rsk-neural skewness of he ndvdual sock, and he rsk-neural skewness of he marke, Skew Skew m, : 3/2,, m, Skew,, = β Skew, (7) where he rsk-neural measures of skewness are esmaed followng Baksh Kapada, and Madan (2003). We provde furher deals n he Appendx. 4 We defne he sysemac and dosyncrac call mpled volales as: CVOL CVOL sys do = β = σ where he beas are esmaed from call and pu mpled volales. We use he correspondng expressons σ ε, m, = σ β σ m,, (8) PVOL, and sys PVOL, when pu mpled volales along wh he correspondng beas are used o do decompose he changes n pu mpled volales. The sysemac vs. dosyncrac decomposon s n erms of sandard devaons and follows Ben-Horan and Levy (1980) and ohers, and s conssen wh our prevous emprcal work lookng a changes n opon volales, raher han varances. We consder he predcve ably of frs-dfference nnovaons sys ΔCVOL, sys ΔPVOL, do ΔCVOL, and 4 Chrsoffersen, Jacobs and Vanberg (2008) argue ha beas compued from opon prces conan dfferen nformaon han beas esmaed from sock reurns. 15

18 do ΔPVOL on he cross secon of sock reurns. As expeced, he cross-seconal correlaon of he nnovaons n he sysemac componen of volales, sys ΔCVOL 0.99, whereas he correlaon beween he dosyncrac erms, and sys ΔPVOL, s very hgh a above do ΔCVOL and do ΔPVOL, s much lower a We repor he sysemac vs. dosyncrac decomposon n Table 6. Snce he correlaon beween sys ΔCVOL and sys ΔPVOL s close o one, we do no use hem smulaneously n one regresson o avod severe mulcollneary. In regressons (1) and (2), he coeffcens on sys ΔCVOL and sys ΔPVOL are sascally nsgnfcan, whereas he coeffcen on do ΔCVOL s posve, remnscen do of he posve coeffcen on ΔCVOL n Tables 2-4. The coeffcen on ΔPVOL s negave, also smlar o he negave coeffcen on ΔPVOL n he prevous cross-seconal regressons, showng ha only he dosyncrac componens are relavely large n magnude and carry hghly sgnfcan - sascs: n regresson (1), he coeffcen on do ΔCVOL s 3.18 wh a -sasc of 4.10 and he coeffcen on do ΔPVOL s 2.43 wh a -sasc of In regresson (2), he coeffcens on do do ΔCVOL and ΔPVOL are almos unchanged wh effecvely he same degrees of sgnfcance. Clearly s changes n he dosyncrac volaly componens ha are drvng he predcably. Regressons (3)-(6) nroduce he same conrol varables as Tables 2-5 and he fndng of ha he predcve componen n he nnovaons of call and pu volaly changes s dosyncrac, no sysemac, s robus. When he oher rsk varables and characerscs are nroduced, here s a decrease n he coeffcen on coeffcen on on do ΔCVOL and do ΔCVOL from 3.2 o around 1.4 and also a smaller decrease n absolue value n he do ΔPVOL from 2.4 o around 2.2. However, n all regressons (3)-(6), he coeffcens do ΔPVOL reman sgnfcan a he 99% level. In summary, he predcve ably of nnovaons n call and pu volales for he cross secon of sock reurns sems from dosyncrac, no sysemac, componens n volales. Ths mples ha s unlkely ha he predcably can be explaned by sysemac rsk premums, a leas from marke-level reurns and aggregae volaly. 16

19 4. Reurns on Volaly Innovaon Porfolos So far we have documened he predcve ably of opon volaly nnovaons for fuure sock reurns by esmang cross-seconal regressons. In hs secon we examne he poenal nvesable reurns ha can be generaed by formng porfolos sored on opon mpled volaly nnovaons. In consrucng porfolos we are necessarly resrced o usng oponable socks. We concenrae on he smples measures of opon volaly nnovaons, ΔCVOL and ΔPVOL Porfolos Ranked on ΔCVOL In Panel A of Table 7 we form qunle 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 5 (Hgh ΔCVOL) ncludes socks wh he hghes changes n call mpled volales n he prevous monh. We equal wegh socks n each qunle porfolo. The frs panel n Table 7 presens he average raw reurns and rsk-adjused reurns of he qunle porfolo reurns over he whole sample from January 1996 o Sepember The CAPM alpha s produced by akng he nercep erm n a regresson of he excess porfolo reurn on he excess value-weghed marke porfolo consruced usng all socks lsed on he NYSE, AMEX, and NASDAQ. We denoe he alpha produced conrollng for he Fama and French (1993) facors by FF3. In FF4 we follow Carhar (1997) and augmen he FF3 model by a momenum facor consruced by Kenneh French. Table 7 also repors he average marke share, monhly change n call mpled volaly (ΔCVOL), monhly radng volume, and open neres of call opons n each qunle porfolo. By consrucon he average monhly ΔCVOL ncreases across he porfolos from 9.47% for qunle 1 o 9.82% for qunle 5. All he -sascs repored n Table 7 are compued wh robus Newey-Wes (1987) sandard errors. Panel A shows he average raw reurn of socks n qunle 1 wh he lowes ΔCVOL s 0.10% per monh and hs monooncally ncreases o 1.07% per monh for socks n qunle 5. The dfference n average raw reurns beween qunles 1 and 5 s 0.97% per monh wh a hghly sgnfcan -sasc of Ths ranslaes o a monhly Sharpe rao of 0.28 and an annualzed Sharpe rao of 0.98 for a sraegy wh monhly rebalancng gong long Hgh ΔCVOL socks and shorng Low ΔCVOL socks. When we perform a CAPM, FF3, and FF4 rsk adjusmen he dfferences n alpha beween qunle porfolos 1 and 5 are remarkably smlar wh approxmaely he same sgnfcance levels. In parcular, he FF4 alpha dfference beween he exreme qunles wh he hghes and lowes ΔCVOL s 0.96% per monh wh a -sasc of For he FF4 facor specfcaon, he exreme qunle alphas are 17

20 hemselves sgnfcan: he Low ΔCVOL FF4 alpha of 0.38% per monh has a -sasc of 2.27 and he FF4 alpha of he Hgh ΔCVOL qunle s 0.58% per monh wh a -sasc of These resuls provde srong evdence for an economcally and sascally sgnfcan, posve relaon beween ΔCVOL and expeced reurns. They complemen he posve coeffcens on ΔCVOL repored n he cross-seconal regressons of Secon 3. In Panel B of Table 7 we oban smlar resuls formng qunle porfolos ranked on he percenage change n call mpled volales, %ΔCVOL. Specfcally, he dfference n raw average reurns beween he hghes and lowes %ΔCVOL porfolos s 0.92% per monh wh a -sasc of The average rsk-adjused reurn dfferences range from 0.88% o 0.93% per monh and are also hghly sgnfcan. We oban a smlar, srong posve lnk beween he call mpled volaly s and average reurns when formng porfolos usng he cross-seconal nnovaons equaon (4). CVOL cs as defned n 4.2. Porfolos Ranked on ΔCVOL and ΔPVOL We found n Secon 3 ha changes n mpled pu volales predced sock reurns bu wh he oppose sgn o call volales. We now examne hs fndng n he conex of producng radable reurns by producng double sors of porfolos ranked on ΔCVOL and ΔPVOL n Table 8. By performng a seres of sequenal sors, we produce he porfolo equvalens of placng boh ΔCVOL and ΔPVOL jonly n a bvarae cross-seconal regresson. In Panel A of Table 8 we perform a sequenal sor frs by creang qunle porfolos ranked by pas ΔPVOL. Then, whn each ΔPVOL qunle we form a second se of qunle porfolos ranked on ΔCVOL. Ths creaes a se of porfolos wh smlar pas ΔPVOL characerscs wh spreads n ΔCVOL and hus examnes expeced reurn dfferences due o ΔCVOL rankngs conrollng for he effec of ΔPVOL. Panel A shows ha n each ΔPVOL qunle, he lower (hgher) ΔCVOL qunles have lower (hgher) average reurns. The column labeled ΔCVOL5 ΔCVOL1 shows he raw reurn dfference beween he Hgh ΔCVOL (ΔCVOL5) and Low ΔCVOL (ΔCVOL1) porfolos whn each ΔPVOL qunle. Whn he lowes ΔPVOL qunle (ΔPVOL1), he average raw reurn ncreases from 0.10% o 1.24% per monh when movng from he frs o he ffh qunles. The average raw reurn dfference beween ΔCVOL5 and ΔCVOL1 s 1.34% per monh wh a Newey-Wes -sasc of Ths paern 18

21 s repeaed across all ΔPVOL qunles and, wh one mnor excepon, he raw reurns are all monooncally ncreasng as ΔCVOL ncreases. 5 Panel A also repors he average reurn dfference beween hghes and lowes qunles ranked on ΔCVOL averaged across he ΔPVOL qunles. Ths average reurn dfference s 1.13% per monh wh a -sasc of Whle he order of magnude s smlar o he raw reurn dfference across exreme qunle porfolos of 0.97% per monh n Panel A, Table 7, he sascal sgnfcance has ncreased n Table 8 when we conrol for he nformaon n ΔPVOL. The dfference n FF3 alphas beween exreme qunle porfolos ranked on ΔCVOL afer conrollng for ΔPVOL s very smlar a 1.12% per monh wh a robus -sasc of In Panel B we repea he same exercse as Panel A bu perform sequenal sors frs on ΔCVOL and hen on ΔPVOL. Ths produces ses of porfolos wh dfferen ΔPVOL rankngs afer conrollng for he nformaon conaned n ΔCVOL. Ths se of sequenal sors produces lower reurns as ΔPVOL ncreases conssen wh he negave coeffcens on ΔPVOL n he cross-seconal regressons. For example, n he frs ΔCVOL1 qunle, he average raw reurns o he qunle wh he hghes (lowes) pas ΔPVOL s 0.27% per monh ( 0.31% per monh). The dfference beween hese exreme qunle reurns s 0.58% per monh, whch s sascally sgnfcan a he 95% level. The negave relaon beween ncreasng ΔPVOL and lower average reurns s repeaed n every ΔCVOL qunle and s mpressvely monooncally decreasng n all cases. Ineresngly, he dfference n average reurns beween he las and frs ΔPVOL qunles s larges for socks whch have experenced he larges changes n CVOL. Ths s seen n he large 1.44% per monh reurn dfference beween he exreme ΔPVOL qunles n he ffh ΔCVOL porfolo. No such skewed paern s observed n Panel A, whch examnes he dfferences n average reurns for ΔCVOL afer conrollng for ΔPVOL. Ths ndcaes ha snce volaly generally ncreases for boh calls and pus (Table 1 shows he correlaon beween ΔCVOL and ΔPVOL s 0.57), here are large ncremenal reurns generaed by shorng socks wh he larges ncreases n call volaly and wh large pu volaly changes. The las wo rows of Table 8, Panel B average he dfferences beween he frs and ffh ΔPVOL qunles across he ΔCVOL qunles. Ths summarzes he reurns o ΔPVOL afer conrollng for ΔCVOL. The average reurn dfference s 0.63% per monh wh a -sasc of The dfference n FF3 alphas s very smlar a 0.68% per monh wh a -sasc of Agan here s a srong negave relaon beween ΔPVOL and sock reurns n he cross secon. 5 We oban smlar resuls when we perform sors usng %ΔCVOL and %ΔPVOL. 19

22 5. Predcng he Cross Secon of Impled Volales wh Sock Reurns Secons 3 and 4 presen srong evdence ha he cross secon of mpled volales conans valuable nformaon o predc he cross secon of sock reurns. In hs secon we examne he oher drecon of predcably and es f sock reurns conan predcve nformaon for he cross secon of mpled and realzed volales. We follow our earler research desgn and examne one of he very smples of varables, he change n he sock reurn, as a proxy for nformaon changes n sock prces, whch s analogous o he change n he mpled volaly for opons. Our emprcal ess dffer sgnfcanly from many sudes n he leraure nvesgang he predcably of opon volales. Many exen sudes focus on me-seres relaons, parcularly beween mpled and realzed volaly a he aggregae ndex level (see, for example, Chrsensen and Prabhala, 1998, and more recenly Chernov, 2007). Bollen and Whaley (2004) examne me-seres predcably of 20 ndvdual opons focusng on ne buyng pressure. Denns and Mayhew (2002) examne cross-seconal predcably of he rsk-neural skewness bu do no examne he cross secon of mpled volales. Goyal and Sareo (2009) documen ha he dfference beween realzed and mpled volales predcs he cross secon of opon reurns. Naurally, our focus on he cross secon of mpled volales does ranslae no opon holdng perod reurns and we use he realzed-mpled volaly spread as a conrol varable, bu our varable of neres s much more smple. We sudy f unusually large reurns n underlyng eques predc he cross secon of mpled volales. We examne he sgnfcance of nformaon spllover from ndvdual socks o ndvdual equy opons based on he frm-level cross-seconal regressons: Δ CVOL = λ + λ Alpha + Conrols + ε, + 1 0, 1,,, + 1 ΔCVOL Δ PVOL = λ + λ Alpha + Conrols + ε,, + 1, + 1 0, 1,,, + 1 (9) where he dependen varables, ΔCVOL and ΔPVOL, denoe he monhly changes n call and pu mpled volales for sock over monh o +1. Alpha s he abnormal reurn (or alpha) for sock over he prevous monh obaned from he CAPM and he hree-facor Fama-French (FF3) model usng specfcaons smlar o regresson (1). The monhly alphas are compued by summng he daly dosyncrac reurns over he prevous monh. To es he sgnfcance of nformaon flow from sock o opons marke, he cross-secon of mpled volaly changes over monh +1 are regressed on he abnormal reurns of ndvdual socks n monh. The frs specfcaon n equaon (9) examnes how call volales over he nex monh respond o sock reurns over he prevous monh n he Alpha erm. The second cross-seconal regresson n 20

23 equaon (9) looks a how call volales move relave o pu volales. Call and pu volaly changes, whle conanng sgnfcanly dfferen nformaon for he cross secon of equy reurns, are correlaed a 0.57 (see Table 1). Thus, call and pu volales end o move n unson for he same frm. Predcng he spread beween pu and call mpled volales, ΔPVOL ΔCVOL, aemps o conrol for he common componen n boh call and pu volales. We delberaely do no use opon reurns as he dependen varable n equaon (9). Opon reurns exhb marked skewness and have pronounced non-lneares from dynamc leverage makng sascal nference dffcul (see, among ohers, Broade, Chernov and Johannes, 2008; Chaudhr and Schroder, 2009). By focusng on mpled volales we avod many of hese nference ssues. The conrol varables we use nclude marke bea, sze, book-o-marke, momenum, llqudy, realzed volaly, and call and pu opon radng volume measures. 6 Followng Bollen and Whaley (2004) and N Pan and Poeshman (2008), we consruc ΔOI C and ΔOI P whch are he changes n he call and pu radng open neres over he prevous monh, respecvely. We also nclude he RV-IV measure and he rsk-neural measure of skewness, QSKEW. Table 9 presens he average slope coeffcens and her Newey-Wes -sascs n parenheses. Table 9 repors ha for boh he CAPM and FF3 alphas, he average slopes on Alpha are posve and sgnfcanly predc boh he call and pu opons mpled volaly changes over he nex monh. We fnd ha opons where he underlyng socks experenced hgh abnormal reurns over he pas monh end o ncrease her mpled volales over he nex monh. Specfcally, a 1% CAPM (FF3) alpha over he prevous monh ncreases call volales by 2.82% (3.68%), on average, wh a hghly sgnfcan - sasc of 2.88 (6.54). Ths shows a shor-erm momenum effec across asse markes wh one-monh sock momenum posvely predcng ncreases n call mpled volales. The posve perssence of lagged sock reurns affecng nex-perod opon volales s he oppose fndng n he leraure of he so-called leverage effec, where volaly ncreases afer pas low reurns (see orgnally Black, 1976). The leverage effec s a me-seres phenomenon where negave s o reurns conemporaneously ncrease curren volaly and snce volaly s perssen, fuure volaly, on he same sock. The predcve relaon n Table 9 s n he cross secon where shor-erm perssence n he sock marke flers hrough o opon markes so ha call opon prces on socks wh hgh pas reurns ncrease nex perod relave o call opons on socks wh low pas reurns. 6 We do no nclude shor-erm reversal (REV) as an addonal conrol varable because of he srong correlaon beween REV and he monhly alphas, whch leads o a severe mulcollneary problem n cross-seconal regressons. The average correlaons among CAPM Alpha, FF3 Alpha, and REV are n he range of 0.92 o Hence, predcng he changes n opons mpled volales wh REV and Alphas produces very smlar resuls. 21

24 Several of he coeffcens on he conrol varables n Table 9 are neresng resuls n her own rgh. As expeced from he one-facor decomposon n equaon (6), beas are posvely relaed o fuure volaly changes n he cross secon. Ths goes beyond he fndng of Duan and We (2009) who show ha opon levels, no changes, are posvely relaed o he proporon of sysemac rsk. Increases n volaly are also larger for small frms and value socks. Underlyng sock momenum, MOM, plays no role n deermnng he cross secon of volaly changes. Conssen wh Goyal and Sareo (2009), opons wh large RV-IV end o predc decreases n mpled volales and so holdng perod reurns on hese opons end o be low. Increases n call and pu open neres srongly predc fuure ncreases n call and pu volales. Fnally, changes n call (pu) mpled volales end o be lower (hgher) for opons where he smle exhbs more pronounced negave skewness. Table 9 also repors resuls for cross-seconally predcng he spread n pu and call volaly changes. A sock wh a CAPM (FF3) alpha of 1% over he pas monh has, on average, changes n call volaly 2.05% (3.34%) hgher han changes n pu volaly. Pu anoher way, momenum n sock reurns over he prevous monh feeds no cross-seconal predcably n opon markes. Posve shorerm sock momenum ends o produce hgher ncreases n call volales relave o pu volales. I should be noed ha from he mpled coeffcens on predcng ΔPVOL n Table 9, whch are posve bu much smaller han he coeffcens on ΔCVOL, ha he mpled volales of boh calls and pus end o ncrease when he underlyng sock has apprecaed. Wha Table 9 also documens s ha call volales ncrease sgnfcanly more han pu volales. We also es wheher he abnormal reurns of ndvdual socks (CAPM, FF3 alphas) can predc he cross-secon of realzed volaly changes: ΔRVOL = λ 0, + λ1, Alpha + Conrols ε 1, (10) where ΔRVOL s he change n realzed reurn volaly of sock usng daly reurns from monh o +1. Table 9 shows ha, afer conrollng for he sock and opon characerscs, he cross-seconal regresson of ΔRVOL on he CAPM alpha yelds an average slope coeffcen of wh a -sasc of Smlar resuls are obaned when he CAPM alpha s replaced by he FF3 alpha; he average slope remans negave a wh a hghly sgnfcan wh a -sasc of These coeffcens are approxmaely en mes larger n absolue value han n he regressons predcng ΔCVOL and ΔCVOL ΔPVOL. The dfferen sgn on lagged Alpha o predc nex-monh ΔRVOL compared o ΔCVOL s surprsng: hgh pas sock reurns predc ncreases n fuure mpled volales ha are no accompaned by ncreases n realzed volales. In fac, fuure realzed volaly ends o declne. 22

25 In summary, Table 9 presens srong evdence of cross-asse class predcably a he monhly frequency from socks o opons. On he one hand, posve prevous monh sock momenum produces ncreases n call volales and hgher call versus pu volales. On he oher hand, posve prevous one-monh sock momenum produces decreases n realzed volales. 6. Economc Inerpreaon The summary of our resuls s ha he cross secon of opons predcs he cross secon of sock reurns and vce versa. Boh drecons of hs predcably nvolve smple changes n prces: changes n opon mpled volales or changes n sock prces over he prevous monh. Socks whch have experenced large posve changes n call opon mpled volaly end o exhb hgh expeced reurns over he nex monh and socks wh large posve s o pu opon mpled volales end o declne over he nex monh. The reurns on porfolos formed by sorng oponable socks ranked by pas changes n call volaly exhb a spread n average reurns and alphas of approxmaely 1% per monh. In he oher drecon, socks wh abnormal reurns of 1% relave o her CAPM bea end o see call mpled volales ncrease over he nex monh by approxmaely 3%. Our fndngs mmedaely rule ou (nosy) raonal expecaons models of underlyng and dervaves n ncomplee markes such as Back (1993), Cao (1999), Burasch and Jlsov (2006), and many ohers. Despe beng non-redundan secures, he prces of opons n hese models mmedaely adjus o any asymmerc or heerogeneous nformaon possessed by agens, or he coss and ncenves of acqurng such nformaon, and hus hese models predc ha here s no predcably from opon o sock markes or vce versa. 7 Our resuls clearly ndcae ha opons and underlyng eques play an mporan role n prce formaon of boh asse markes. Our emprcal fndngs are parly conssen wh he mcrosrucure sequenal rade model of Easley, O Hara and Srnvas (1998) n whch unnformed lqudy raders place orders n he equy marke, he opons marke, or boh. Opon markes are no always venues for nformaon-based raders f nformed raders canno sasfacorly hde her rades, bu f a leas some 7 Much of hs leraure focuses on he effecs of nroducng opons no ncomplee marke economes. Because of asymmerc nformaon, Back (1993) and Bas and Hllon (1994) show ha nroducng an opon can cause underlyng sock volaly o become sochasc and sgnfcanly ncrease. Mos recenly, Cao and Yang (2009) show ha when opons are nroduced when agens have dfferences of opnon, radng volumes reflec he dfferences of agens opnon bu all asse prces are formed as f a represenave nvesor exsed whose belef reflecs he average belefs across all nvesors. These ssues are no emprcally relevan for our resuls because we have focused on sock reurns for whch opons already exs. 23

26 nformed nvesors choose o rade n opons before radng n underlyng socks, hen opon prces wll predc fuure sock prce movemens. Conversely, f sock markes are more lqud and nformed raders can more easly hde her rades n eques, hen sock markes may lead opon markes. Easley, O Hara and Srnvas fnd evdence ha opon volumes of ceran ypes of rades forecas fuure sock prces whn he nex hour usng nraday daa. Movaed from he Easley, O Hara and Srnvas model, Cremers and Wenbaum (2009) show ha devaons from pu-call pary documen ha opon prces can predc sock prces by several days. One key nsgh of he frs mcrosrucure nformaon-based model of Glosen and Mlgrom (1985) s ha he radng process reveals underlyng nformaon and affecs he fuure pah of prces. How fas hs prce adjusmen occurs s a key ssue. All mcrosrucure models lke Easley, O Hara and Srnvas (1998) are desgned o operae a hgh frequences and he marke maker s adjusmen o nformed rades s exponenally fas n erms of he numbers of subsequen rades and snce rades for socks wh opons occur rapdly, ceranly exremely fas n chronologcal me. The predcably we uncover of he cross-seconal predcably of equy reurns by opons and vce versa are a he monhly frequency. Ths s a greaer challenge o he mcrosrucure models whch are desgned o work a hgh, usually nra-day, frequences. We follow an older leraure ha debaes wheher opons or socks lead or lag each oher. However, hese sudes were conduced prmarly a he daly frequency. Manaser and Rendleman (1982), Bhaacharya (1987), and Anhony (1988) fnd ha opons predc fuure sock prces. Flemng, Osdek and Whaley (1996) documen opons lead he underlyng markes usng fuures and opons on fuures. In conras, Sephan and Whaley (1990) and Chan, Chung and Johnson (1993) fnd sock markes lead opon markes. Chakravary, Gulen and Mayhew (2004) fnd ha boh socks and opon markes conrbue o prce dscovery. They fnd he conrbuon of opon markes o he oal varance of common, permanen prce movemens s around 20%, whch s conssen wh nformed nvesors radng n boh sock and opon markes and opons playng an mporan role n prce formaon. Our fndngs are very dfferen from hs leraure because we fnd ha opon volaly nnovaons conan srong predcve power for he cross secon of equy reurns a he much lower monhly frequency. Smlarly, we fnd a remarkable predcably of pas one-monh sock reurns for fuure mpled volales a he monhly frequency. A more recen leraure uses he sandard monhly frequency common n he cross-seconal leraure o examne how opon nformaon predcs underlyng sock reurns. Ths leraure ncludes Ofek, Rchardson and Whelaw (2004), Bal and Hovakman (2009), Cremers and Wenbaum (2009), and Xng, Zhang, and Zhao (2009), who documen he predcve ably of varous sascs compued 24

27 from he cross secon of opons can predc fuure equy reurns. Our analyss conrolled for some of hese effecs, n parcular he opon skew examned by Conrad, Dmar, and Ghysels (2009) and Xng, Zhang and Zhao (2009). None of hese papers documen ha frs-dfference nnovaons and oher more sophscaed me-seres and cross-seconal measures of rsk-neural volales predc fuure reurns. Ths s a surprsngly smple, and srongly sgnfcan, measure of news arrvng n opons markes. Of course, we also fnd a smple measure of news pas equy reurns forecass fuure opon volales. Our resuls on he predcably of equy reurns by opon nformaon are parly conssen wh a more recenly developed srand of leraure whch advocaes ha nvesor demand for an opon can affec s prce. Bollen and Whaley (2004) buld a demand-based opon model for seng opon prces and show ha an excess of buyer-movaed raders cause opon prces and mpled volaly o rse and an excess of seller-movaed rades wll cause mpled volaly o fall. They show emprcally ha conemporaneous changes n daly mpled volales are drven by varous measures of ne buyng pressure. Buldng on hs work, Garleanu, Pedersen and Poeshman (2009) develop an equlbrum model where he end-user demand of opons affecs he prces of opons because rsk-averse nermedares who ake he oher sde of end-users canno perfecly hedge her opon posons. They convncngly show ha here s a srong emprcal conemporaneous relaon beween opon expensveness and end-user demand for ndex and ndvdual equy opons. 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. If he end-users of opons, whose demand drves opon prces, have an nformaon advanage and choose o rade n opons over socks, hen opon prces wll frs reac and lead underlyng sock prces. Thus, nformed dervave end-users who have nformaon ha he sock wll end o apprecae wll choose o buy calls or sell pus, causng large changes n call opon volales o predc fuure sock prce apprecaon. Smlarly, f pu opon sellers hold nsde nformaon ha he sock wll declne n he fuure, hey wll drve up he prce of pu opons, or sell calls, and socks wh large changes n pu volales wll lead sock prce deprecaons. For our resuls o be conssen wh demand-based models of opon prces requres ha he margnal ne buyers or sellers of opons are nformed and choose o place her nformed rades n opon markes raher han sock markes. As Easley, O Hara and Srnvas (1998) pon ou, gven he much greaer lqudy of he sock marke s no clear ha nformed raders would choose opon markes n whch o camouflage her rades. Furhermore, he nformaon dssemnaon mus be relavely slow as o occur a he monhly frequency. The resuls we documen of pas sock reurns nfluencng fuure opon prces ndcae ha some nformed radng acvy does ake place frs n sock markes. One dfferen aspec of he cross- 25

28 seconal predcably of opon volales s ha opons, by defnon, allow speculaors o ake posons on only he volaly of sock prces whou needng o ake vews on wheher sock prces wll rend up or down. I s unclear why here should be so much cross-seconal spllover from shor-erm sock momenum n he prevous monh o ncreases n opon values over he nex monh. Moreover, our resuls show ha he predcably n mpled volales s oppose n sgn o he predcably of realzed volales. Informed volaly raders havng nsde nformaon on volaly are unlkely o frs ake posons n underlyng equy markes, whch do no drecly embed volaly rsk as a frs-order effec compared o he sensvy of opon prces o volaly nformaon. A possble raonal mechansm o explan he cross-seconal predcably of opon volales by pas sock reurns s ha shor-erm momenum ncreases uncerany and hs uncerany s refleced n hgher opon volales. I s possble ha an alernave sory o explan our resuls would rely on behavoral underreacon. A se of fas-reacng, and probably beer nformed agens, rade n boh opon and underlyng equy markes. In he case of opons predcng socks, hese nvesors choose o rade n opon markes causng he mpled volales of calls o quckly jump up on posve news and drve up he mpled volales of pus on he arrval of negave news on he underlyng sock. Invesors n he sock marke do no ake no accoun he nformaon news n opon markes. These nvesors may respond more slowly o nformaon, or he nformaon slowly dffuses o hese nvesors, smlar o he segmened nvesors of Hong and Sen (1999). Ths causes he opon marke o reac frs followed by he sock marke and would gve rse o changes n call (pu) volales predcng fuure sock reurns o ncrease (decrease). Applyng an under-reacon sory o he cross-momenum effec of shor-erm prce apprecaon predcng fuure ncreases n opon volales s more challengng because expeced reurns of sock prces can be hedged ou under raonal opon prcng models. Anoher cavea o such a behavoral model s ha mos under-reacon sores apply o longer horzons han one monh, such as he Jegadeesh and Tman (1993) momenum effec over he nex 1-12 monhs. The cross-seconal shor-erm reversal effec of Jegadeesh (1990) and Lehmann (1990) s generally explaned by over-reacon n mos behavoral models (see Subrahmanyam, 2005). We confrm hs predcably n Secon 3 wh negave, bu nsgnfcan, coeffcens on REV. Thus, a canddae behavoral model should explan he underreacon of sock markes o opon nformaon, he spllover ncrease n opon volales from shorerm sock momenum, and smulaneously accoun for he shor-erm over-reacon of sock reurns o sock marke nformaon. 26

29 7. Concluson We documen a remarkable ably of opon volales o predc he cross secon of sock reurns and he sock reurns o predc he cross secon of opon volales. In he drecon of opons o equy reurns, socks wh pas large nnovaons n call opon mpled volales posvely predc fuure sock reurns whle socks wh prevous large changes n pu mpled volales predc low sock reurns over he nex monh. Ths cross-seconal predcably of sock reurns from opon volaly nnovaons s hghly sascally sgnfcan boh n cross-seconal regressons and porfolo reurns. The effec s robus o he usual rsk facors and characersc conrols, usng conrol varables drawn from boh equy and opon markes, and appears n subsample perods ncludng he mos recen fnancal crss. When qunle porfolos are creaed ranked on pas frs-dfferences n call volales, he spread n average reurns and alphas beween he frs and ffh porfolos s approxmaely 1% per monh. In he oher drecon of lagged equy reurns o opon volales, opons wh underlyng eques ha have large prce apprecaons end o ncrease n prce over he nex perod. In parcular, a 1% reurn relave o he CAPM over he prevous monh causes opon mpled volales o ncrease by around 3% and he ncrease n volales s larger for call opons han for pu opons. A he same me, fuure realzed volales are predced o declne whle opon volales end o rse. These effecs are n excess of he co-movemens of nex-monh opon volaly changes wh several lagged crossseconal sock and opon characerscs. Our resuls sugges ha boh opon and equy markes news evens, as proxed by smple frs dfferences n opon volales and pas changes n sock prces, play mporan roles n prce formaon of each ohers markes. The predcve drecon of opons o socks s conssen wh demand-based models of opon prces where he nformed end-users of opons choose o place her orders n opon markes raher han sock markes. Bu he connuaon of shor-erm momenum n opon prces by pas one-monh sock reurns ndcaes ha mporan prce effecs mpac sock markes frs. The overall resuls are conssen wh he slow dffuson of nformaon across opon and equy markes wh beer nformed agens radng n boh markes. 27

30 Appendx: Esmang Beas from Opon Informaon We use he resuls n Baksh Kapada, and Madan (2003) and Duan and We (2009) o oban an esmae of a sock s marke bea from he cross secon of opons. Baksh Kapada, and Madan (2003) nroduce a procedure o exrac he volaly, skewness, and kuross of he rsk-neural reurn densy from a group of ou-of-he-money call and pu opons. Duan and We (2009) use he resuls n Baksh Kapada, and Madan (2003) and defne he rsk-neural marke bea as a funcon of he rsk-neural skewness of ndvdual socks and he rsk-neural skewness of he marke. Le he τ-perod connuously compounded reurn on he underlyng asse S, be R ( τ ) = ln[ S ( + τ ) / S ( )]. Le τ Q E represen he expecaon operaor under he rsk-neural measure. The me- prce of a quadrac, cubc, and quarc payoff receved a me +τ can be wren as V Q rτ 2 Q rτ 3 Q rτ 4 ( τ ) = E [ e R ( ) ], W ( τ ) = E [ e R ( ) ], and X ( τ ) = E [ e R ( ) ], respecvely, where r s τ τ τ he consan rsk-free rae. Baksh Kapada, and Madan (2003) show ha he τ-perod rsk-neural varance and skewness are Var Q rt 2 ( τ ) e V ( τ ) μ ( τ ) = (A.1) Skew 3 e W ( τ ) 3 μ ( τ) e V ( τ) + 2 μ ( τ) ( ). rt rt Q,,,,, τ = rt 2 3/2 e V, ( τ) μ, ( τ) The expressons V ( ), W ( ), and X ( ) are gven by: V τ τ τ S 2(1 ln( K / S )) 2(1 ln( K / S )) ( τ ) = C ( τ; K ) dk + P 2 2 K S K 0 X W ( τ ) = ( τ ) = + + S S 0 S, S, 0 6ln( K 6ln( K 12[ln( K 12[ln( K / S / S / S / S ) 3[ln( K K K 2 ) 3[ln( K )] )] 2 K 2 K 2 4[ln( K 2 4[ln( K 2 / S / S / S / S )] )] 2 2 )] )] C P 3 3 C P ( τ ; K ) dk ( τ ; K ) dk ( τ; K ) dk ( τ; K ) dk ( τ; K ) dk (A.2) (A.3) (A.4) (A.5) rt rt rt rt e V, ( τ ) e W, ( τ) e X, ( τ) μ, ( τ ) = e 1, (A.6)

31 where C ( τ ; K ) and P ( τ ; K ) are he me- prces of European call and pu opons wren on he underlyng sock S wh a srke prce K and expraon dae of τ. We follow Denns and Mayhew (2002) and use he rapezodal approxmaon o compue he negrals n equaons (A.1) and (A.2) for ou-ofhe-money call and pu opons across dfferen srke prces and use he Volaly Surface daa on sandardzed opons wh he hree-monh T-bll reurn for he rsk-free rae. Q Duan and We (2009) show ha he rsk-neural skewness of an ndvdual sock, Skew, ( τ ), s Q relaed o he rsk-neural skewness of he marke, Skew, ( τ ), hrough he relaon Skew m ( τ) = β ( τ) Skew, (A.7) Q 3/2 Q, m, Q where Skew, ( τ ) and Skew Q, ( τ ) are esmaed usng equaon (A.2). In our emprcal analyses, we use m Volaly Surface sandardzed call and pu opons wh τ=30 days o maury o esmae he sock bea from equaon (A.7). We use Volaly Surface daa on he S&P500 ndex o compue he rsk-neural marke skewness. 29

32 References Amhud, Yakov, 2002, Illqudy and sock reurns: Cross-secon and me-seres effecs, Journal of Fnancal Markes 5, Amn, Kaushk I., and Charles M. C. Lee, 1997, Opon radng, prce dscovery, and earnngs news dssemnaon, Conemporary Accounng Research 14, Ang, Andrew, Rober J. Hodrck, Yuhang Xng, and Xaoyan Zhang, 2006, The cross-secon of volaly and expeced reurns, Journal of Fnance 61, Ang, Andrew, Rober J. Hodrck, Yuhang Xng, and Xaoyan Zhang, 2009, Hgh dosyncrac volaly and low reurns: Inernaonal and furher U.S. evdence, Journal of Fnancal Economcs 91, Anhony, Joseph H., 1988, The nerrelaon of sock and opons marke radng-volume daa, Journal of Fnance 43, Back, Kerry, 1993, Asymmerc nformaon and opons, Revew of Fnancal Sudes 6, Bal Turan G., and Armen Hovakman, 2009, Volaly spreads and expeced sock reurns, Managemen Scence 55, Baksh Gurdp, Nkunj Kapada, and Dlp Madan, 2003, Sock reurn characerscs, skew laws, and he dfferenal prcng of ndvdual equy opons, Revew of Fnancal Sudes 16, Bekaer, Geer, and Guojun Wu, 2000, Asymmerc volaly and rsk n equy markes, Revew of Fnancal Sudes 13, Ben-Horm, Moshe, and Ham Levy, 1980, Toal rsk and nondversfable rsk: A pedagogc noe, Journal of Fnancal and Quanave Analyss 2, Bhaacharya, Mhr, 1987, Prce changes of relaed secures: The case of call opons and socks, Journal of Fnancal and Quanave Analyss 22, Bas, Bruno, and Perre Hllon, 1994, Insder and lqudy radng n sock and opon markes, Revew of Fnancal Sudes 74, Black, Fscher, 1975, Fac and fanasy n he use of opons, Fnancal Analyss Journal 31, Black, Fscher, 1976, Sudes of sock prce volaly changes, Proceedngs of he 1976 Meengs of he Amercan Sascal Assocaon, Busness and Economc Sascs Secon, Black, Fscher, and Myron Scholes, 1973, The prcng of opons and corporae lables, Journal of Polcal Economy 81, Bollen, Ncolas P. B., and Rober Whaley, 2004, Does ne buyng pressure affec he shape of mpled volaly funcons? Journal of Fnance 59,

33 Broade, Mark, Mkhal Chernov, and Mchael Johannes, 2009, Undersandng ndex opon reurns, Revew of Fnancal Sudes 22, Burasch Andrea, and Alexe Jlsov, 2006, Model uncerany and opon markes wh heerogeneous belefs, Journal of Fnance 61, Cao, Charles, Zhwu Chen, and John M. Grffn, 2005, The nformaonal conen of opon volume pror o akeovers, Journal of Busness 78, Cao, Henry H., 1999, The effec of dervave asses on nformaon acquson and prce behavor n a raonal expecaons equlbrum, Revew of Fnancal Sudes 12, Cao, Henry H., and Hu Ou-Yang, 2009, Dfferences of opnon of publc nformaon and speculave radng n socks and opons, Revew of Fnancal Sudes 22, Carhar, Mark M., 1997, On perssence n muual fund performance, Journal of Fnance 52, Chakravary, Sugao, Huseyn Gulen, and Sewar Mahew, 2004, Informed radng n sock and opon markes, Journal of Fnance 59, Chan, Kalok, Y. Peer Chung, and Wa Mng Fong, 2002, The nformaonal role of sock and opon volume, Revew of Fnancal Sudes 15, Chan, Kalok, Y. Peer Chung, and Herb Johnson, 1993, Why opon prces lag sock prces: A radng based explanaon, Journal of Fnance 48, Chaudhr Ranadeb, and Mark Schroder, 2009, Monooncy of he sochasc dscoun facor and expeced opon reurns, Workng paper, Mchgan Sae Unversy. Chernov, Mkhal, 2007, On he role of rsk prema n volaly forecasng, Journal of Busness and Economc Sascs 25, Chrsensen, Ben, and Nagpurnanand R. Prabhala, 1998, The relaon beween mpled and realzed volaly, Journal of Fnancal Economcs, 50, Chrsoffersen, Peer F., Krs Jacobs, and Gregory Vanberg, 2008, Forward-lookng beas, Workng paper, McGll Unversy. Conrad, Jennfer, Rober F. Dmar, and Erc Ghysels, 2009, Ex ane skewness and expeced sock reurns, Workng Paper. Unversy of Norh Carolna a Chapel Hll and Unversy of Mchgan. Cremers, Marjn, and Davd Wenbaum, 2009, Devaons from pu-call pary and sock reurn predcably, Journal of Fnancal and Quanave Analyss forhcomng. Deemple, Jerome, and Larry Selden, 1991, A general equlbrum analyss of opon and sock marke neracons, Inernaonal Economc Revew 32, Damond, Douglas W., and Rober E. Verrecha, 1987, Consrans on shor-sellng and asse prce adjusmen o prvae nformaon, Journal of Fnancal Economcs 18,

34 Duan, Jn-Chuan, and Jason We 2009, Sysemac rsk and he prce Srucure of ndvdual equy opons, Revew of Fnancal Sudes 22, Denns, Parck, and Sewar Mayhew, 2002, Rsk-neural skewness: Evdence from sock opons, Journal of Fnancal and Quanave Analyss 37, Easley, Davd, Maureen O Hara, and P.S. Srnvas, Opon volume and sock prces: Evdence on where nformed raders rade, Journal of Fnance 53, Fama, Eugene F., and Kenneh R. French, 1992, Cross-secon of expeced sock reurns, Journal of Fnance 47, Fama, Eugene F., and Kenneh R. French, 1993, Common rsk facors n he reurns on socks and bonds, Journal of Fnancal Economcs 33, Fama, Eugene F., and James D. MacBeh, 1973, Rsk and reurn: Some emprcal ess, Journal of Polcal Economy 81, Fglewsk Sephen, and Xaozu Wang, 2000, Is he leverage effec a leverage effec? Workng Paper, New York Unversy. Flemng, Jeff, Barbara Osdek, and Rober Whaley, 1996, Tradng coss and he relave raes of prce dscovery n sock, fuures, and opon markes, Journal of Fuures Markes 16, Garlenau, Ncolae, Lasse H. Pedersen, and Allen M. Poeshman, 2009, Demand-based opon prcng, Revew of Fnancal Sudes, forhcomng. Glosen, Lawrence R., and Paul R. Mlgrom, 1985, Bd, ask and ransacon prces n a specals marke wh heerogeneously nformed raders, Journal of Fnancal Economcs 14, Goyal, Am and Alesso Sareo, 2009, Cross-secon of opon reurns and volaly, Journal of Fnancal Economcs 94, Grossman, Sanford J., 1977, The exsence of fuures markes, nosy raonal expecaons and nformaon exernales, Revew of Economc Sudes 44, Hong, Harrson, and Jeremy C. Sen, 1999, A unfed heory of underreacon, momenum radng, and overreacon n asse markes, Journal of Fnance 54, Hong, Harrson, Terence Lm, Jeremy C. Sen, 2000, Bad news ravels slowly: Sze, analys coverage, and he profably of momenum sraeges, Journal of Fnance 55, Jegadeesh, Narasmhan, 1990, Evdence of predcable behavor of secury reurns, Journal of Fnance 45, Jegadeesh, Narasmhan, and Sherdan Tman, 1993, Reurns o buyng wnners and sellng losers: Implcaons for sock marke effcency, Journal of Fnance 48,

35 Shasr Kuldeep, Raman Kumar and Aulya Sarn, 1992, The behavor of opon prce around large block ransacons n he underlyng secury: Some emprcal evdence on ner-marke fronrunnng, Journal of Fnance 47, Lehmann, Bruce, 1990, Fads, marngales, and marke effcency, Quarerly Journal of Economcs 105, Loughran, Tm, 1997, Book-o-marke across frm sze, exchange, and seasonaly: Is here an effec? Journal of Fnancal and Quanave Analyss 32, Manaser, Seven, and Rchard J. Rendleman, 1982, Opon prces as predcors of equlbrum sock prces, Journal of Fnance 37, Newey, Whney K., and Kenneh D. Wes, 1987, A smple, posve sem-defne, heeroskedascy and auocorrelaon conssen covarance marx, Economerca 55, N Sophe, Jun Pan, and Allen Poeshman, 2008, Volaly nformaon radng n he opon marke, Journal of Fnance 63, Ofek, E., M. Rchardson, and R. Whelaw, 2004, Lmed arbrage and shor sale consrans: Evdence from he opon markes, Journal of Fnancal Economcs 74, Pan, Jun, and Allen M. Poeshman, 2006, The nformaon n opon volume for fuure sock prces, Revew of Fnancal Sudes 19, Subrahmanyam, Avandhar, Rchard Roll, and Eduardo Schwarz, 2009, Opons radng acvy and frm valuaon, Journal of Fnancal Economcs 94, Sefan, Jens A., and Rober E. Whaley, 1990, Inraday prce change and radng volume relaons n he sock and sock opon markes, Journal of Fnance 45, Subrahmanyam, Avandhar, 2005, Dsngushng beween raonales for shor-horzon predcably n sock reurns, Fnancal Revew 40, Vanden, Joel M., 2008, Informaon qualy and opons, Revew of Fnancal Sudes 21, Xng, Yuhang, Xaoyan Zhang, and Ru Zhao, 2009, Wha does ndvdual opon volaly smrks ell us abou fuure equy reurns? Journal of Fnancal and Quanave Analyss forhcomng. 33

36 Table 1. Descrpve Sascs of Impled Volales Panel A presens he average number of socks per monh for each year from 1996 o Average and sandard devaon of he monhly call and pu mpled volales (CVOL, PVOL) are repored for each year from 1996 o The las row presens he overall averages. The annualzed mpled volales are obaned from he Volaly Surface a OponMercs and cover he perod from January 1996 o Sepember Panel B repors he average frm-level cross-correlaons of he levels and changes n mpled volales, he levels and changes n realzed volaly, and me-seres and cross-seconal s o mpled volales. Panel A. Summary Sascs for he Call and Pu Impled Volales CVOL PVOL Dae # of socks Average Sdev Average Sdev Average

37 Table 1 (connued) Panel B. Average Frm-Level Correlaons CVOL s PVOL s CVOL cs PVOL cs CVOL PVOL ΔCVOL ΔPVOL RVOL ΔRVOL CVOL 1 PVOL ΔCVOL ΔPVOL RVOL ΔRVOL CVOL s PVOL s CVOL cs PVOL cs 35

38 Table 2. Predcng Equy Reurns by Frs Dfferences n Impled Volales Ths able presens he average slope coeffcens and her Newey-Wes (1987) adjused -sascs n parenheses from he frm-level Fama-MacBeh (1973) he cross-seconal regressons n equaon (5) for he sample perod of January 1996 o Sepember The onemonh ahead reurns of ndvdual socks are regressed on he level, change, and percen change n realzed, call, and pu mpled volales obaned from sandardzed a-he-money opons wh 30 days o maury. (1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) CVOL ( 0.77) PVOL ( 1.41) RVOL ( 1.53) ΔCVOL (2.90) (5.02) ΔPVOL ( 2.09) ΔRVOL (0.30) %ΔCVOL (3.63) %ΔPVOL ( 3.27) %ΔRVOL ( 0.90) ( 5.32) (5.76) ( 6.84) 36

39 Table 3. Predcng Equy Reurns by Frs Dfferences n Impled Volales: Subsample Analyss Ths able presens he average slope coeffcens and her Newey-Wes adjused -sascs n parenheses from he frm-level Fama-MacBeh (1973) cross-seconal regressons n equaon (5) of equy reurns on he changes n call and pu mpled volales for he full sample and subsample perods. The call and pu mpled volales are obaned from a-he-money opons wh 30 days o maury. Jan 1996 Sep 2008 Jan 1996 Dec 2001 Jan 2002 Sep 2008 Jan 2008 Sep 2008 ΔCVOL (5.02) (4.16) (2.78) (1.73) ΔPVOL ( 5.32) ( 2.62) ( 3.66) ( 2.93) 37

40 Table 4. Predcng Equy Reurns by Frs Dfferences n Impled Volales and Oher Predcors Ths able presens he frm-level cross-seconal regressons n equaon (5) of equy reurns on he monhly changes n call and pu mpled volales (ΔCVOL and ΔPVOL, respecvely) afer conrollng for marke bea (BETA), log marke capalzaon (SIZE), log book-o-marke rao (BM), momenum (MOM), llqudy (ILLIQ), shor-erm reversal (REV), realzed sock reurn volaly (RVOL), he log call-pu rao of opon radng volume (C/P Volume), he log rao of call-pu open neres (C/P OI), he realzed-mpled volaly spread (RV-IV), and he rsk-neural measure of skewness (QSKEW). Monhly cross-seconal regressons are run wh he changes n call and pu mpled volales for a-he-money opons wh expraons of 30 and 91 calendar days. The average slope coeffcens and her Newey-Wes -sascs are repored n parenheses. 30 days o maury 91 days o maury (1) (2) (3) (4) (5) (6) ΔCVOL (5.02) (3.27) (2.52) (6.86) (5.70) (5.26) ΔPVOL ( 5.32) ( 4.46) ( 4.45) ( 6.67) ( 5.79) ( 6.02) BETA (0.31) ( 0.05) (0.41) (0.07) SIZE ( 1.18) ( 0.43) ( 1.40) ( 0.58) BM (0.61) (0.87) (0.63) (0.88) MOM (1.51) (1.34) (1.49) (1.34) ILLIQ (0.55) (0.30) (0.59) (0.32) REV ( 1.79) ( 1.79) ( 1.51) ( 1.50) RVOL ( 3.11) ( 3.09) C/P Volume (1.68) (1.72) (2.11) (2.00) C/P OI (0.03) (0.51) ( 0.41) (0.19) RV-IV ( 1.37) ( 1.92) QSKEW ( 5.16) ( 4.75) ( 4.58) ( 4.04) 38

41 Table 5. Predcng Equy Reurns by Tme-Seres and Cross-Seconal Impled Volaly Innovaons Ths able presens he average slope coeffcens and her Newey-Wes adjused -sascs n parenheses from he frm-level Fama-MacBeh (1973) cross-seconal regressons n equaon (5) for he sample perod of January 1996 o Sepember The one-monh ahead reurns of ndvdual socks are regressed on he monhly nnovaons n call and pu mpled volales obaned from a-he-money opons wh 30 days o maury. In he lef panel, he monhly nnovaons n mpled volales are generaed based on he me-seres AR(1) model esmaed for each frm usng he pas wo years of monhly daa (see equaon (3)). In he rgh panel, he monhly nnovaons n mpled volales are generaed based on he frm-level cross-seconal regressons of mpled volales on her one-monh lagged values esmaed for each monh n our sample (see equaon (4)). Tme-Seres Innovaons Cross-Seconal Innovaons (1) (2) (3) (4) (5) (6) CVOL (4.02) (2.94) (2.95) (3.81) (3.14) (2.53) PVOL ( 3.45) ( 5.05) ( 4.94) ( 6.69) ( 5.26) ( 5.73) BETA (0.20) (0.07) (0.35) (0.01) SIZE ( 2.01) ( 1.79) ( 1.28) ( 0.58) BM ( 0.44) ( 0.26) (0.60) (0.85) MOM (1.45) (1.42) (1.52) (1.36) ILLIQ ( 0.23) ( 0.29) (0.61) (0.38) REV ( 1.55) ( 1.51) ( 1.85) ( 1.86) RVOL ( 1.27) ( 3.01) C/P Volume (0.64) (0.62) (1.94) (2.06) C/P OI (0.53) (0.58) ( 0.05) (0.38) RV-IV ( 0.52) ( 1.01) QSKEW ( 3.41) ( 3.34) ( 5.27) ( 5.09) 39

42 Table 6. Predcng Reurns by Sysemac and Idosyncrac Volaly Shocks Ths able presens he average slope coeffcens and her Newey-Wes (1987) adjused - sascs n parenheses from he frm-level Fama-MacBeh (1973) cross-seconal regressons n equaon (5) for he sample perod of January 1996 o Sepember The one-monh ahead reurns of ndvdual socks are regressed on he sysemac and dosyncrac componens of he changes n call and pu mpled volales and he conrol varables. ΔCVOL sys, ΔCVOL do, ΔPVOL sys, and ΔPVOL do are defned n equaon (8) and are obaned from a-he-money call and pu opons wh 30 days o maury usng he mehod oulned n he Appendx. (1) (2) (3) (4) (5) (6) ΔCVOL sys (1.51) (0.31) (0.28) ΔCVOL do (4.10) (4.11) (2.95) (2.90) (2.95) (2.90) ΔPVOL sys (1.27) (0.10) (0.07) ΔPVOL do ( 4.42) ( 4.46) ( 3.80) ( 3.84) ( 3.84) ( 3.88) BETA ( 0.10) ( 0.11) ( 0.10) ( 0.11) SIZE ( 1.36) ( 1.29) ( 1.36) ( 1.30) BM (0.19) (0.22) (0.19) (0.22) MOM (1.39) (1.37) (1.39) (1.37) ILLIQ (0.89) (0.85) (0.89) (0.86) REV ( 2.16) ( 2.14) ( 2.17) ( 2.15) RVOL ( 2.61) ( 2.60) C/P Volume (1.16) (1.15) (1.16) (1.15) C/P OI (1.17) (1.17) (1.17) (1.17) RV-IV ( 2.63) ( 2.62) QSKEW ( 5.42) ( 5.39) ( 5.43) ( 5.40) 40

43 Table 7. Porfolos Ranked on Impled Call Volaly Innovaons Ths able presens he average raw reurns, average rsk-adjused reurns (CAPM, FF3 alpha, FF4 alpha, where FF3 denoes he Fama and French (1993) model and FF4 augmens he Fama-French model wh a momenum facor), average marke share, average monhly change n call mpled volales (ΔCVOL) of oponable socks, and average monhly radng volume ( 10-3 ) and average open neres of call opons n he equalweghed qunle porfolos ha are formed by sorng socks based on ΔCVOL and %ΔCVOL. Porfolo 1 (Low ΔCVOL) conans socks wh he lowes monhly changes n call mpled volales n he prevous monh and Porfolo 5 (Hgh ΔCVOL) ncludes socks wh he hghes monhly changes n call mpled volales n he prevous monh. The row Avg. 5-1 Dff. repors he dfference n average raw and rskadjused reurns beween he Hgh ΔCVOL and Low ΔCVOL qunles. Newey-Wes adjused -sascs are repored n parenheses. The sample perod s from January 1996 o Sepember Panel A. Porfolos Ranked on ΔCVOL Reurn CAPM Alpha FF3 Alpha FF4 Alpha Mk share ΔCVOL Tradng Volume Open Ineres Low ΔCVOL Hgh ΔCVOL Avg. 5-1 Dff sa. (3.37) (3.59) (3.37) (3.18) Panel B. Porfolos Ranked on %ΔCVOL Reurn CAPM Alpha FF3 Alpha FF4 Alpha Mk share ΔCVOL Tradng Volume Open Ineres Low %ΔCVOL Hgh %ΔCVOL Avg. 5-1 Dff sa. (4.07) (4.33) (4.33) (4.20) 41

44 Table 8. Porfolos Ranked on Impled Call and Pu Volaly Innovaons In Panel A, qunle porfolos are frs formed every monh from January 1996 o Sepember 2008 by sorng he oponable socks based on he monhly changes n pu mpled volales (ΔPVOL). Then, whn each ΔPVOL qunle, socks are sored no qunle porfolos ranked based on he monhly changes n call mpled volales (ΔCVOL) so ha ΔCVOL1 (ΔCVOL5) conans socks wh he lowes (hghes) ΔCVOL. The column labeled ΔCVOL5 ΔCVOL1 shows he average raw reurn dfference beween Hgh ΔCVOL (ΔCVOL5) and Low ΔCVOL (ΔCVOL1) porfolos whn each ΔPVOL qunle. Raw reurn dfferences are averaged across he fve ΔPVOL qunles o produce qunle porfolos wh dsperson n ΔCVOL, bu smlar dsperson n ΔPVOL. Panel B performs a smlar procedure bu frs sequenally sors on ΔCVOL and hen on ΔPVOL. The row labeled Average Reurn Dff. repors he average raw reurn dfference beween he Hgh ΔCVOL and Low ΔCVOL porfolos afer conrollng for ΔPVOL. The 5-1 dfferences n he FF3 alpha, produced usng he Fama and French (1993) model, are repored n he las row. Newey-Wes -sascs are repored n parenheses. Panel A. Porfolos Ranked Frs on ΔPVOL and hen on ΔCVOL ΔCVOL1 ΔCVOL2 ΔCVOL3 ΔCVOL4 ΔCVOL5 ΔCVOL5 ΔCVOL1 ΔPVOL (4.17) ΔPVOL (4.40) ΔPVOL (4.11) ΔPVOL (4.26) ΔPVOL (2.80) Average Reurn Dff (5.39) FF3 Alpha Dff (4.95) Panel B. Porfolos Ranked Frs on ΔCVOL and hen on ΔPVOL ΔPVOL1 ΔPVOL2 ΔPVOL3 ΔPVOL4 ΔPVOL5 ΔPVOL5 ΔPVOL1 ΔCVOL ( 2.04) ΔCVOL ( 0.73) ΔCVOL ( 1.86) ΔCVOL ( 3.28) ΔCVOL ( 4.76) Average Reurn Dff ( 4.81) FF3 Alpha Dff ( 5.51) 42

45 Table 9. Informaon Flow from Indvdual Socks o Indvdual Equy Opons Ths able presens he sgnfcance of nformaon spllover from sock o opons marke based on he abnormal reurns of ndvdual socks and he changes n opons mpled volales and he changes n realzed volaly. The frs hree columns repor resuls based on he CAPM Alphas and he las hree columns presen resuls based on he FF3 Alphas. The dependen varables are nex-monh changes n call volales, ΔCVOL, he change n call volales relave o pu volales, ΔCVOL ΔPVOL, and he change n realzed volales, ΔRVOL. The average slope coeffcens and her Newey-Wes -sascs from he frm-level cross-seconal regressons are repored for equaons (9)-(10). The conrol varables nclude marke bea (BETA), log marke capalzaon (SIZE), log book-o-marke rao (BM), momenum (MOM), llqudy (ILLIQ), realzed-mpled volaly spread (RV-IV), change n he call open neres (ΔOI C ), change n he pu open neres (ΔOI P ), and he rsk-neural skewness (QSKEW). The monhly alphas are calculaed by summng he daly alphas n a monh. The Alphas are esmaed based on he CAPM and he hree-facor Fama-French model (FF3) usng daly reurn observaons over he prevous monh. Newey-Wes adjused -sascs are repored n parenheses. The sample perod s from January 1996 o Sepember CAPM Alpha FF3 Alpha ΔCVOL- ΔCVOL- ΔCVOL ΔPVOL ΔRVOL ΔCVOL ΔPVOL ΔRVOL Alpha (2.88) (3.21) ( 6.17) (6.54) (6.51) ( 7.67) BETA (2.78) (2.43) ( 4.82) (2.48) (1.77) ( 6.04) SIZE ( 4.62) ( 5.74) ( 6.34) ( 7.28) ( 11.39) ( 9.29) BM (1.97) (3.06) ( 2.72) (3.22) (4.03) ( 2.16) MOM (0.67) (0.23) ( 0.44) ( 0.24) ( 5.59) (0.38) ILLIQ (2.70) (2.88) (5.33) (7.92) (3.79) (7.18) RV-IV ( 5.50) ( 1.73) (40.75) ( 7.04) (0.14) (50.13) ΔOI C (5.80) (2.28) (4.63) (7.63) (0.47) (8.78) ΔOI P (4.64) ( 2.54) (7.87) (14.13) ( 2.79) (13.70) QSKEW ( 9.40) ( 7.64) ( 4.03) ( 9.54) ( 9.62) ( 5.89) 43