The Information Content of Implied Skewness and Kurtosis Changes Prior to Earnings Announcements for Stock and Option Returns

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1 The Informaion Conen of Implied kewness and urosis Changes Prior o Earnings Announcemens for ock and Opion Reurns Dean Diavaopoulos Deparmen of Finance Villanova Universiy James. Doran Bank of America Professor of Finance Deparmen of Finance Florida ae Universiy Andy Fodor Deparmen of Finance Ohio Universiy David R. Peerson Wachovia Professor of Finance Deparmen of Finance Florida ae Universiy Absrac We explore wheher changes in sock reurn skewness and kurosis as implied in opion prices preceding earnings announcemens provide informaion abou subsequen sock and opion reurns hrough he announcemen. We demonsrae ha he change in implied skewness and kurosis can be relaed o changing jump risk premiums where jump risk can be associaed wih he uncerainy around he direcion and size of he sock price response o he earnings announcemen. As such implied skewness kurosis should capure he direcion magniude of a sock jump if opion prices change as a resul of changing jump risk. We find implied skewness and kurosis prior o earnings announcemens have srong predicive power for fuure sock and opion reurns even afer conrolling for implied volailiy. 1

2 The Informaion Conen of Implied kewness and urosis Changes Prior o Earnings Announcemens for ock and Opion Reurns I. Inroducion Undersanding how informaion flows beween differen markes such as he opion and sock markes is an imporan finance opic. As saed by Black 1975 An invesor who wans he acion on a sock has wo ways of geing i. He can deal direcly in he sock or he can deal in he opion. Black 1975 also suggess ha raders wih privae informaion prefer o exploi ha informaion by rading in he opions marke. He argues ha opion markes provide lower shor selling coss and higher leverage and ha many poenial informaion raders will rade in he opions marke when hey may no rade a all in he absence of opion markes. The likely resul is ha informaion is refleced in opion prices before i is refleced in sock prices. 1 Evidence in Bali and Hovramahin 008 Cremers and Weinbaum 008 Diavaopoulos e al. 008 and Zhang e al. 008 is consisen wih Black s conclusion. We add o he lieraure by focusing on a period of ime immediaely preceding earnings announcemen daes and examining if opion prices provide informaion abou fuure sock and opion reurns. Earnings announcemens are ofen rich in informaion conen. Mos of he analysis of he earnings announcemens ceners on sock reurns on he even days or he subsequen period. Abnormal reurns following he even days are ypically referred o as he pos earnings announcemen drif. We specifically analyze wheher changes in sock reurn skewness and kurosis as implied in opion prices before he earnings announcemen are relaed o fuure sock and opion reurns. 1 Many sudies address he general lead-lag relaion beween opion and sock prices. For example Manaser and Rendelman 198 posi ha opion markes may provide a preferred oule for informed invesors. They find ha he closing prices of call opions conain informaion abou equilibrium sock prices ha is no conained in he closing prices of he underlying socks. heikh and Ronn 1994 find ha opion reurns conain sysemaic paerns even afer adjusing for paerns in he means and variances of he underlying asses. This is consisen wih he hypohesis ha informed rading in opions can make he opions marke informaive abou he value of he underlying asse. For example Beaver 1968 Ball and Brown 1968 Landsman and Maydew 00 and Baalio and Mendenhall 005 are jus a few of he numerous sudies ha examine announcemen day effecs and pos earnings announcemen drif.

3 We argue ha implied skewness and kurosis are likely o be a leas as valuable in providing informaion abou fuure earnings as he implied variance. Wih respec o he presence of opions mos lieraure on sock reurns and earnings announcemens addresses differences in sock reurns beween opion and nonopion firms. In paricular Jennings and arks 1986 kinner 1990 Ho 1993 and Mendenhall and Fehrs 1999 find ha firms wih raded opions end o have quicker price responses and smaller surprises han hose ha do no. This suggess ha opion lising improves he informaional efficiency of he marke for he underlying sock. Amin and Lee 1997 find ha rading volume in opions increases by more han 10% in he four days before quarerly earnings announcemens while rading volume in socks increases by less han 5% providing furher suppor for increased efficiency for socks wih lised opions. They also find ha opion raders iniiae a greaer proporion of long shor posiions immediaely before good bad earnings news. This suggess ha informed raders may prefer o deal in opions when hey have an imporan piece of informaion consisen wih Black s 1975 hypohesis. Oher sudies invesigae he role of sock reurn volailiy implied in opion prices and he relaion wih fuure sock reurns. Paell and Wolfson find ha implied volailiy as calculaed from he Black and choles 1973 pricing model increases before earnings announcemens and decreases following hem. Zhang e al. 008 use implied sock reurn volailiies from opions o focus on he general predicabiliy and informaion conen of volailiy skews for fuure equiy reurns. As an aside hey presen evidence ha he shape of he volailiy skew is relaed o he surprise in earnings announcemens wih firms wih he seepes volailiy smirks experiencing he wors earnings surprise in subsequen monhs. The findings in Paell and Wolfson and Zhang e al. 008 imply wo specific relaions beween he opion and sock markes; firs opion raders increase he price and volailiy of an opion prior o an earnings announcemen and second he shape of he volailiy skew may imply he direcion of he announcemen. We exend he finding in hese prior works in hree imporan ways. Firs we focus on changes versus levels of implied momens because implied parameers should change as he opions marke anicipaes he size and direcion of he approaching announcemen. econd we 3

4 separae he volailiy skew change ino he nd 3 rd and 4 h momens of he implied disribuion o relae he given momen o he direcion and magniude of he anicipaed sock price response. Third we focus on sock and opion reurns prior o and a earnings announcemens versus earnings surprises which may reveal a poenial rading sraegy. We expec ha he price response of a sock o good or bad news on he day of an earnings announcemen poses significan risk o he shor opions rader especially if he opion is close o expiraion. This risk is a funcion of no only he direcion of he news and he resuling sock price response bu also he magniude of he informaion and relaed sock jump. The rader can adjus o hese risks by increasing he price of all opions via increasing he volailiy used o price he opions or alering he volailiy of hose ha are mos a risk i.e. ou-of-he-money opions. We relae hese risks o he momens implied in he risk-neural disribuion. In oher words do opion prices embed accurae expecaions abou he direcion and magniude of fuure sock price movemen associaed wih earnings announcemens? The former may be measured by he expeced sock reurn skewness ha is implied in opion prices and he laer by he implied kurosis. The purpose of his sudy is o deermine if implied skewness and kurosis are useful for predicing fuure sock and opion reurns preceding and a earnings announcemens. pecifically beginning 30 rading days prior o an earnings announcemen we calculae changes in implied skewness and kurosis over various periods and examine subsequen sock and opion reurns. In so doing we provide direc evidence on wheher imporan informaion a earnings announcemens is incorporaed in opion prices before he announcemen and he value of ha informaion for earning fuure reurns. We sor securiies based on heir wo-day buy-and-hold reurns BHRs over he earnings announcemen dae day 0 and he following rading day day 1. We find a direc relaion beween hese BHRs and changes in implied skewness and kurosis measured from days -30 hrough -5. We hen sor securiies ino five groups based on skewness changes over hree differen inervals preceding earnings announcemens and separaely sor on kurosis changes. In boh cases he fuure BHRs beginning he day afer he change hrough day 1 are significanly greaer for he high change quinile han 4

5 he low change quinile. Thus skewness and kurosis changes predic fuure reurns. These predicive abiliies hold even afer we conrol for implied volailiy. We perform five-by-five double sors on changes in implied skewness and kurosis and find ha he BHRs of he high skewness change group ouperform hose of he low skewness change group across kurosis change quiniles bu he significan reurn differences are more concenraed in he higher kurosis change quiniles. The BHRs of he high kurosis change group significanly ouperform hose of he low kurosis change group only for he wo highes skewness change groups. These resuls indicae ha changes in boh implied skewness and kurosis conribue o reurn predicabiliy bu he relaions end o be sronges for high skewness and kurosis change socks. We nex examine call and pu BHRs following changes in implied skewness and kurosis. As wih sock we find srong evidence ha hese changes can predic opion reurns. Finally we esimae firm-level regressions wih sock call and pu BHRs as dependen variables. Independen variables include skewness and kurosis changes an ineracion erm beween hese wo variables and a se of conrol variables. We find ha sock and call reurns beginning afer skewness and kurosis changes and coninuing hrough day 1 are significanly relaed o he changes. Pu reurns are relaed o prior skewness changes bu only very weakly relaed o kurosis changes. Overall informaion abou fuure earnings announcemens embedded in implied skewness and kurosis is relaed o fuure sock and opion reurns. This sudy is developed in he following secions. ecion II presens our mehodology and moivaion including he mehods of esimaing implied skewness and kurosis changes and a discussion of our daa. Empirical resuls are provided in ecion III and ecion IV concludes. II. Mehodology and Moivaion A. Measures of Implied kewness and urosis Our hypohesis is ha informaion abou earnings announcemens is embedded in opion prices prior o he announcemen and ha his informaion is useful for predicing 5

6 sock reurns. 3 A ypical approach in earnings announcemen sudies is o focus on abnormal sock reurns. If opion prices predic sock reurns however he price of an opion will reflec he anicipaed changes in he sock price which may be relaed o he jump premium. The sock price change is comprised of abnormal and normal reurns. Thus we examine oal sock reurns a and preceding he earnings announcemen. 4 If informaion abou earnings announcemens is presen in opion prices prior o he announcemen hen compared o a base period we expec wo effecs o occur ha can affec opion prices. Firs if he direcion of he price response o an earnings announcemen is anicipaed hen we expec implied skewness o change. If a posiive negaive jump occurs hen he implied skewness should become more posiive negaive. In oher words ou-of-he-money OTM calls pus will increase relaive o a-he-money ATM opions if a posiive negaive jump is expeced. To capure he informaion in implied skewness we employ he non-parameric measure of Bakshi e al Implied skewness is defined as: EW r 3e μ υ + μ 3 r e υ μ r e W = 1 where r is he risk free rae is he ime oday is he ime a expiraion and W μ and υ are defined in Appendix A. This measure expresses implied skewness as a single value by using informaion in boh OTM calls and pus providing a simple alernaive o dividing he skew ino pars. udies such as Doran e al. 007 Dimar e al. 008 and Agarwal e al. 008 demonsrae ha his measure is informaive for 3 Under his hypohesis wo ypes of sock price adjusmen processes may no be fully funcioning. Firs if he sock marke anicipaes earnings informaion he way he opions marke does hen sock prices should also adjus. Therefore he sock marke is responding o informaion abou earnings less efficienly han he opions marke. econd even if sockholders know nohing abou earnings opion prices are adjusing. Therefore invesors could iniiae rades using he pu-call pariy relaion beween socks and opions o bring sock prices ino line. However he pu-call pariy adjusmen may no be fully working. One reason may be ha sric pu-call pariy holds only for European opions and we are using American opions for which a pu-call pariy inequaliy holds. This allows a looser relaion beween prices of socks and opions. Also invesors who ry o exploi he relaion beween sock and opion prices as indicaed by pu-call pariy migh be faced wih large ransacion coss and bid-ask spreads. These impedimens could cause he sock price adjusmen process o lag behind he opion price adjusmen process. 4 Benchmark reurns are likely small over a wo-day announcemen window. Thus he oal sock reurn a he announcemen is likely very close o and highly correlaed wih he wo-day abnormal reurn. 6

7 idenifying poenial marke crashes capuring asses bubbles and explaining hedge fund reurns respecively. The second effec ha changes opion prices may be a resul of he uncerainy of he sock price response. This occurs if opion raders are worried abou a large sock price response bu are unsure of he direcion. Here we expec ha boh OTM calls and pus will increase relaive o ATM opions or here will be an increase in densiy in he ails of he implied disribuion. To capure implied kurosis we use he measure calculaed in Bakshi e al. 003 given as URT r r 4e μ W + 6e μ υ 3μ r e υ μ r e X = 4 where X is defined in Appendix A. Unlike prior sudies which focus primarily on he second and in more limied fashion he hird momen we feel here is significan informaion in he fourh momen. Pan 00 and Bakshi and Cao 008 show ha incorporaing jumps in he underlying daa generaing process is criical for fiing he reurn disribuion of boh sock and opion prices. Even more criical is he noion of a jump risk premium capuring he difference beween he implied and risk neural disribuions or he difference beween opion and sock prices. This jump premium canno be fully capured by implied skewness since skewness implies a direcion. The jump premium may be relaed o he inensiy of a jump which is capured by kurosis. 5 ince our analysis is concerned wih how informaion is incorporaed in implied skewness and kurosis we focus on he change in boh hese measures. Using an iniial poin in ime ω and a subsequen poin in ime Ω we calculae he level of implied skewness and kurosis from equaions 1 and for boh periods. The change over he period is given as 5 everal sudies including Paell and Wolfson and Zhang Zhao and Xing 008 focus on implied variances. An implied variance may no be he bes measure of he value of informaion however because i will naurally increase as he earnings announcemen dae approaches due o he imminen uncerainy. Much of our analysis conrols for implied variances and his allows us o focus on he anicipaed direcion skewness and magniude kurosis of fuure sock reurns. 7

8 ΔEWω Ω = EWΩ EW ω 3 ΔURTω Ω = URTΩ URT ω 4 As a conrol we also calculae he change in implied volailiy over he same periods since we wan o disinguish beween he informaion conen of each momen. The iniial poin ω of he momen change measures is 30 rading-days prior o he earnings announcemen dae day 0. Thiry rading-days prior o he earnings announcemen represens our base period where we hypohesize here is lile if any informaion abou he fuure earnings announcemen embedded in sock or opion prices. There are hree differen ending poins Ω of he momen change measures. These are 0 10 and 5 rading-days prior o he earnings announcemen dae. We examine hese muliple ime horizons o deermine no only if informaion is capured in he implied momens bu how ha informaion evolves over ime. If direcional informaion is conained in hese implied momens hen we expec higher posiive negaive implied skewness changes for firms wih he highes lowes reurns on he earnings announcemen dae and he following rading day days 0 and 1. If here is increased jump uncerainy we expec higher kurosis changes for firms wih boh he lowes and highes reurns over hese periods. Following he skewness and kurosis changes over he windows idenified above we examine subsequen sock and opion BHRs hrough day 1. We examine wheher here is a relaion beween he skewness and kurosis changes and subsequen reurns. B. Daa To es for wheher skewness and kurosis changes are relaed o he sock price response prior o and hrough he earnings announcemen daily sock reurn share price and shares ousanding daa are colleced from CRP for he period January 1996 hrough April Earnings announcemen daes day 0 are obained from Compusa as well as he book value of equiy. The sample is resriced o firms wih raded opions a leas 6 ETFs foreign and financial firms uiliies and securiies wih share codes oher han 10 or 11 are excluded. 8

9 30 rading days prior o an earnings announcemen dae. There are 4746 firms and 7407 announcemen daes in he sample. Daily implied volailiy and opion price daa are colleced from OpionMerics. 7 A sandardized implied volailiy is calculaed as he moneyness weighed implied volailiy where ATM opions are given he mos weigh. III. Empirical Resuls A. Analysis Based on ingle ors In he firs par of our analysis we divide he sample ino deciles based on sock BHRs over days 0 and 1. For each earnings announcemen we calculae values of EW and URT a rading-days and -30 and hen he respecive changes from -30 o and -5. We expec greaer posiive negaive skewness changes for firms in he higher lower BHR deciles if invesors in he opions marke correcly anicipae he direcion of earnings announcemens. We expec greaer posiive kurosis changes in boh he higher and lower BHR deciles if invesors in he opions marke anicipae a jump bu are unsure of he direcion. When calculaing EW and URT for each company we use he opions wih expiraions having as shor a mauriy as possible subjec o following day 1. These near-erm opions should bes reflec he informaion conen of earnings announcemens. Mean values for BHRs over days 0 and 1 and implied skewness kurosis and volailiy levels a days and -30 are repored in Table 1 Panel A. The high minus low column in Panel A shows ha for days and -0 implied skewness significanly increases from low o high earnings announcemen BHRs; he relaion is significan a he 1% level for days -5 and -10 and a he 5% level for day -0. The relaion is insignifican for day -30. This shows he opions marke begins o anicipae informaion in earnings announcemens a leas 0 rading-days beforehand. All four implied kurosis measures end o peak for he middle BHR deciles. Neverheless for days -5 and -10 here are significan increases in implied kurosis from he low o he high BHR caegory. This is somewha surprising since our expecaion is ha kurosis should increase for a poenial jump irrespecive of direcion. The difference beween he high 7 We consider all firms wih any raded opion. Addiionally we examine a smaller sub-sample of firms ha have non-zero opion volume and find similar resuls. 9

10 and low BHR deciles for days -5 and -10 suggess ha kurosis may be imporan for call opions bu no pu opions. Implied volailiy shows negligible change from low o high BHR deciles wih slighly lower levels for middle BHR deciles. This volailiy paern explains some of he kurosis paern. ince kurosis is calculaed as he fourh momen divided by he second momen squared low levels of volailiy for middle BHR deciles can be linked o high levels of kurosis for he same deciles. For exreme BHR deciles volailiy is relaively unchanged. Thus changes in kurosis from he low o he high decile are due o fourh momen changes no second momen changes. Changes in implied skewness kurosis and volailiy from day -30 o days and -5 are repored in Panel B. The resuls are consisen wih hose in Panel A. Changes in implied skewness and kurosis are significanly greaer a he 5% level or beer for he high BHR decile han for he low BHR decile in all caegories; in paricular he high-low differences for all skewness and kurosis changes are posiive and saisically significan. The differences are numerically larger for greaer lenghs of ime. Thus opion prices begin o reflec he informaion conen of earnings announcemens as he announcemen dae approaches. These resuls are imporan because hey sugges ha opion raders rea anicipaed posiive and negaive jumps differenly. 8 ince he kurosis changes are greaes in he high BHR deciles his furher suggess differen informaion for calls and pus. Differences in volailiy changes across BHR deciles are very small. For all fuure analyses we group earnings announcemens by he monh in which hey are made. We form averages of characerisics abou hese announcemens by his monhly sysem and hen form grand averages over our full sample period. This procedure minimizes effecs of good or bad news clusering in ime over he full period. If opion prices reflec earnings informaion prior o he announcemen implied skewness and kurosis changes should be sronger for closer mauriy opions provided all expiraions follow he announcemen. This is because jump risk is highes for opions closes o expiraion. In Table skewness and kurosis changes are presened by opion expiraion. This able compares curren opions wih he firs expiraions following he 8 If invesors end o buy more calls han pus hen opion raders are faced wih higher jump risk for posiive informaion evens. 10

11 announcemen monh opions o hose ha have he nex expiraion monh +1 opions. 9 Each monh firms wih an earnings announcemen are divided ino quiniles according o BHRs. In Panels A and B firms are divided according o BHRs over he period -41 and skewness and kurosis changes are repored over days Differences in skewness and kurosis beween he wo opion expiraions are expressed as he absolue value of he monh opions minus he absolue value of he monh +1 opions. Thus a posiive difference indicaes a greaer response for he monh opions. 10 kewness change differences should be larges in low bad news and high good news quiniles. Negaive skewness changes should be seen in he low deciles wih posiive changes in he high deciles. urosis changes should be posiive across all quiniles and differences beween expiraions should also be posiive. Resuls in Panel A show ha all of he skewness changes have he expeced signs. The differences in absolue values beween he wo expiraions are larges for quiniles 1 and 5 also as expeced. However none of he differences are saisically significan. All kurosis changes are posiive and he differences beween expiraions are all posiive and significan a he 1% level; all kurosis resuls are as expeced. We hen repea he analysis wih reurns over he period -91 and skewness and kurosis changes over he period Resuls are presened in Panels C and D and are virually idenical o hose in Panels A and B. Finally we analyze reurns over he period -191 and skewness and kurosis changes over he period Resuls are in Panels E and F and again are virually idenical o findings in Panels A and B. As a whole resuls in Table are consisen wih he hypohesis ha informaion abou earnings is refleced in opion prices prior o he earnings announcemen. Paerns of implied kurosis are srongly supporive of his conclusion while paerns of implied skewness offer much weaker suppor. We now focus on near-erm opions and sock BHRs following implied skewness and kurosis changes hrough day kewness and kurosis changes are measured over he ime periods and Each monh announcing firms are 9 Mos bu no all of hese subsequen expiraion daes are one monh beyond he closer expiraion daes. 10 The direcion of he response in a given comparison is always he same for he wo expiraions. 11 All opions expire afer he earnings announcemen. Conrolling for when he opion expires afer he announcemens does no change he resuls. 11

12 ranked by skewness and kurosis changes over each of hese hree inervals and placed ino equal-weighed porfolio quiniles and subsequen BHRs are calculaed. Mean daily values over he sample period of BHRs for each quinile and high minus low quiniles are provided along wih he average skewness and kurosis changes. kewness resuls are presened in Table 3 Panel A and urosis resuls are in Table 3 Panel B. The difference in BHRs beween high and low quiniles is posiive and saisically significan across all skewness and kurosis change ime horizons and subsequen reurn periods. For example wih skewness changes over days an invesor long socks in he high skewness change quinile would realize an average daily 0.3 basis poin reurn gain over an invesor long socks in he low skewness change quinile. ince a large posiive kurosis change can occur for eiher posiive or negaive anicipaed sock price jumps a kurosis change alone canno explain he posiive BHR differences across high and low kurosis change quiniles. Neverheless our kurosis change resuls in Table 1 Panel B show ha he kurosis change for negaive jumps low BHR deciles and no jumps middle BHR deciles are very similar. Therefore he large posiive kurosis changes observed in Table 3 Panel B are likely due o anicipaed posiive jump announcemens. The resuls in Table 3 suppor our hypohesis ha opion prices reflec earnings informaion prior o he announcemen. Following opion price changes sock prices reac in a consisen direcion hrough he earnings announcemen. B. Analysis Based on Double ors I is possible ha volailiy or changes in volailiy he second momen may be affecing our resuls. I is naural for implied volailiy o increase prior o earnings announcemens because of he impending uncerainy. As noed wih he discussion of Table 1 resuls kurosis is defined as he fourh momen divided by he squared second momen; hus volailiy and kurosis may be inversely relaed. Furher skewness is defined as he hird momen divided by he second momen raised o he 1.5 power; so skewness and volailiy may be inversely relaed. Therefore o correcly idenify he impacs of he hird and fourh momens he second momen needs o be conrolled for. If he posiive relaion of skewness and kurosis changes wih fuure reurns is caused by he second momen hen once i is conrolled for hese relaions should vanish. 1

13 We employ a double-soring procedure o conrol for volailiy and volailiy changes. Each monh we sor socks ino quiniles based on eiher implied volailiy changes. Volailiy is calculaed as he moneyness weighed implied volailiy for opions where ATM opions receive he mos weigh. Then we furher sor socks ino quiniles based on eiher implied skewness or kurosis changes. kewness kurosis and volailiy changes are measured over he same hree inervals sudied before and Volailiy levels are observed a days and -0. Equal-weighed porfolio BHRs are examined over periods and -191 like before. Mean BHRs are provided in Table 4 Panel A for implied skewness changes and Panel B for implied kurosis changes. High minus low BHRs are also presened. kewness resuls are robus o volailiy conrols. The difference in BHRs beween high and low skewness change quiniles is posiive for all volailiy and volailiy change quiniles across all reurn periods and significan for all bu one volailiy change quinile. However he BHR differences are greaes in he high volailiy and volailiy change quiniles. The resuls for kurosis are similar o hose for skewness. All volailiy quiniles and all bu one of he volailiy change quiniles have posiive high minus BHRs; mos are saisically significan. This shows ha he posiive and significan relaion beween kurosis and fuure reurns is mainained afer conrolling for volailiy effecs. imilar o skewness he BHR differences based on kurosis are greaes in he high volailiy and volailiy change quiniles. Thus implied volailiy levels and changes are no responsible for our deeced abiliy of opion prices o incorporae informaion abou upcoming earnings announcemens hrough implied skewness and kurosis changes. We nex invesigae wheher he srong implied skewness and kurosis relaions we have found are unique effecs or if one subsumes he oher. Each monh we sor socks ino quiniles based on implied skewness changes and hen ino quiniles based on implied kurosis changes. This enables us o see if kurosis changes maer afer conrolling for skewness changes. We hen sor firs on kurosis change and hen on skewness change allowing us o deermine if skewness change maers afer conrolling for kurosis change. The same change periods are used as before. BHRs are examined 13

14 for he same subsequen periods as previously. They are presened in Table 5 wih he skewness change firs sors in Panel A and he kurosis change firs sors in Panel B. In Panel A BHRs for high minus low kurosis change quiniles are negaive bu mosly insignifican for he hree lowes skewness change quiniles bu posiive and generally significan a he 5% level or beer for he wo highes skewness change quiniles. In Panel B BHRs for high minus low skewness change quiniles are posiive for all kurosis change quiniles bu he relaion ends o be sronges for he higher kurosis change quiniles. Thus resuls in Table 5 sugges ha boh implied skewness and kurosis have he abiliy o independenly predic BHRs hrough earnings announcemens bu he informaion conen seems o be concenraed in higher skewness change and kurosis change socks. In he lower wo skewness change quiniles he BHRs for he high minus low kurosis change quiniles are negaive bu generally insignifican. The negaive relaion is no unexpeced because low skewness change socks are likely associaed wih bad news. For hese firms high kurosis change socks should do worse han low kurosis change socks. C. Opion Reurns ince here is subsanial evidence ha changes in implied skewness and kurosis imbedded in opion prices can predic sock reurns we nex examine if hey can also predic call and pu reurns. We measure skewness and kurosis changes and subsequen reurns over he same hree periods as in prior analyses. Opion reurns are weighed according o midpoin prices and are calculaed by buying a he ask price and selling a he bid. Equal-weighed BHRs for skewness and kurosis change quiniles and for he high minus low quiniles are calculaed wih means and medians presened in Table 6. 1 BHRs are shown for ATM and OTM calls and pus. ATM opions have he raio of he sock price o he exercise price beween 0.95 and OTM calls pus have he same raio greaer han 1.1 less han 0.9. BHRs following skewness changes are in Panel A and hose following kurosis changes are in Panel B. For all caegories of call pu opions high minus low skewness and kurosis changes have posiive negaive BHRs. For call opions all high minus low differences 1 Medians are examined because opion reurns are highly skewed. 14

15 are significan a he 5% level or higher. For pu opions all high minus low skewness change differences are significan a he 1% level. Wih OTM pu opions all high minus low kurosis change differences are significan a he 1% level whereas for ATM pu opions half he differences are significan a he 5% level or beer. The resuls srongly suppor he hypohesis ha informaion abou fuure earnings announcemens as refleced hrough implied skewness and kurosis can predic fuure opion reurns. These findings are consisen wih hose found for he predicion of sock reurns. D. Regressions As our final analysis we examine if he abiliy of implied skewness and kurosis o predic sock and opion reurns disappears afer conrolling for common crosssecional reurn predicors. We esimae cross-secional regressions of sock and opion reurns on he marke value of equiy IZE book-o-marke equiy BM momenum MOM and day or -0 moneyness weighed implied volailiy IV implied skewness EW and implied kurosis URT. 13 Oher independen variables include he change from day -30 o day or -0 in implied volailiy ΔIV implied skewness ΔEW and implied kurosis ΔURT and he ineracion of ΔEW and ΔURT ΔEWURT. Regressions include dummy variables conrolling for firms. BHRs for sock and ATM call and pu opions over he periods and -191 are he dependen variables. 14 Opion BHRs are weighed according o he midpoin price and are calculaed by buying a he ask price and selling a he bid. Regression esimaion resuls are in Table 7 wih Panel A for sock Panel B for calls and Panel C for pus. The empirical specificaions is RHPR i = α + β1izei + βbm i + β3momi + β4ivi + β5δivi + β6 EW + β 7 URTi + β8δewi + β9δurti + β10δewurti + ε i 13 i 13 The marke value of equiy is measured a he end of he monh prior o day -30. Book equiy is measured as in Fama and French 199 and momenum is measured as reurns over he prior 1 monhs. 14 OTM opions provide similar resuls. 15

16 where R HPR i is he BHR for eiher he sock call or pu for firm i. The firs model resrics β β β β β β β 0 he second model resrics β β 0 he hird = 9 10 = model resrics β β 0 he fourh model resrics β β 0 and he fifh model has no 8 10 = 8 9 = resricions. For he sock regressions ΔEW ΔURT and ΔEWURT end o have posiive and significan relaions wih fuure BHRs. This is always rue when one of he hree is in he model wihou he presence of he oher wo and is ypically rue when all hree are included ogeher despie possible collineariy beween he measures. The hree variables are imporan despie he inclusion of Δ IV which iself is ypically a posiive and significan explanaory variable. There is also evidence ha IV EW and URT have a significanly posiive effec on BHRs especially for he wo longer holding periods. Thus resuls in Panel A confirm prior evidence of he abiliy of changes in implied skewness and kurosis o predic sock reurns preceding and a earnings announcemens. Call regression resuls in Panel B are similar o hose for sock. ΔEW ΔURT and ΔEWURT end o have posiive relaions wih call BHRs. This is always rue when one of he hree is in he model wihou he presence of he oher wo wih he excepion of ΔEWURT in he shores holding period. ΔEWURT has a significan effec on he longes period BHRs bu i ends o weaken as he holding period shorens. The conrol variable Δ IV ends o affec BHRs for he shores holding period while IV ends o affec BHRs for he longer periods. Consisen wih sock reurn paerns and afer conrolling for implied volailiy call opion prices hrough implied skewness and kurosis conain informaion abou fuure earnings announcemens. Pu regression resuls in Panel C are slighly weaker han for sock and call reurns. In he shores holding period implied skewness and kurosis changes are no significanly relaed o fuure BHRs. ΔEW is an imporan explanaory variable for he longer wo holding periods. The coefficien on ΔURT is significan only for he longes holding period. ΔEWURT is a significan explanaory variable in he middle-lengh holding period probably due o he influence of ΔEW. Implied volailiy and volailiy changes end o be significan conrol variables. Thus informaion 16

17 abou fuure earnings is presen in pu prices prior o he announcemen mainly as refleced in implied skewness. This implies he effec of skewness and kurosis changes impacs call and pu prices differenly. IV. Conclusion We examine wheher informaion abou fuure earnings announcemens is embedded in opion prices hrough implied skewness and kurosis prior o he announcemen. kewness should capure he anicipaed direcion of he informaion or fuure sock move while kurosis should reflec he anicipaed magniude of he informaion or size of he sock jump. To es wheher implied skewness and kurosis can capure a jump even measures of implied skewness and kurosis calculaed from Bakshi e al. 003 are applied o 7407 earnings announcemens made by 4746 firms. We examine BHRs following he skewness and kurosis changes hrough he earnings announcemen. Our porfolio analysis shows ha boh implied skewness and kurosis changes srongly predic fuure sock reurns hrough he earnings announcemen. The predicive abiliy is sronger for opions expiring soon afer he announcemen han for laer mauriy opions. kewness and kurosis changes can predic fuure sock reurns across all levels of and changes in implied volailiy. The abiliy of implied kurosis changes o predic sock reurns is primarily confined o socks wih greaer changes in implied skewness. imilarly he abiliy of skewness changes o predic sock reurns is weaker for low kurosis change socks. Thus he sronges sock reurn predicive abiliy is associaed wih higher skewness and kurosis change socks. kewness and kurosis changes also srongly predic reurns for ATM and OTM call and pu reurns. Finally using individual firm s sock and opions we cross-secionally regress BHRs on changes in implied skewness and kurosis an ineracion of he wo changes and a se of conrol variables. For sock and call opions we find ha changes in implied skewness and kurosis are srongly relaed o subsequen reurns. For pu opion reurns we find ha skewness change is an imporan explanaory variable bu kurosis changes have a very weak effec. 17

18 Overall our resuls show ha over a period of ime prior o earnings announcemens implied skewness and kurosis changes are srongly relaed o fuure sock and opion reurns hrough he earnings announcemen dae. This indicaes ha informed raders affec opion prices before he public announcemen and in a manner ha predics fuure sock and opion reurns. Our resuls sugges ha idenifying implied skewness and kurosis changes prior o earnings announcemens may be profiable for invesors and reflecive of marke inefficiency. I remains o be seen if such opporuniies exis for oher anicipaed evens. 18

19 19 Appendix A: Expressions for Risk-Neural kewness The model-free esimaes of risk-neural skewness are based on Bakshi apadia and Madan 003. Le log log R + and } { μ R E Q. EW is defined as: A.1 and URT is equal o: A. where A.3 where r is he risk free ineres rae is he ime oday is he ime a expiraion is he srike price is he curren sock price C is he call price and P is he pu price. The price of he cubic and quaric conracs are A.4 A.5 Finally μ X e W e v e e r r r r A } { } { μ ν μ ν μ μ μ e e W e R E R E EW r r r Q Q + = ; log 1 ; log 1 0 d P d C ν + + =. ; log 4 log 1 ; log 4 log 1 ; log 3 6log ; log 3 6 log d P d C X d P d C W + = + = } { } { μ ν μ ν μ μ μ μ e e W e X e R E R E URT r r r r Q Q + =

20 References Amin.I. Lee C.M.C Opion rading price discovery and earnings news disseminaion. Conemporary Accouning Research Agarwal V. Bakshi G. Huij J Dynamic invesmen opporuniies and he crosssecion of hedge fund reurns: implicaions of higher-momen risks for performance. Universiy of Maryland working paper. Baalio R.H. Mendenhall R.R Earnings expecaions invesor rade size and anomalous reurns around earnings announcemens. Journal of Financial Economics Bakshi G. Cao C Risk-neural kurosis jumps and opion pricing: evidence from mos acively raded firms. Universiy of Maryland working paper. Bakshi G. apadia N. Madan D ock reurn characerisics skew laws and differenial pricing of individual equiy opions. Review of Financial udies Bali T. Hovakimian A Volailiy spreads and expeced sock reurns. Baruch working paper. Ball R. Brown P An empirical evaluaion of accouning income numbers. Journal of Accouning Research Beaver W The informaion conen of annual earnings announcemens. Journal of Accouning Research upplemen Black F Fac and fanasy in he use of opions. Financial Analyss Journal Black F. choles M The pricing of opions and corporae liabiliies. Journal of Poliical Economy Cremers.J.M. Weinbaum D Deviaions from pu-call pariy and sock reurn predicabiliy. Journal of Financial and Quaniaive Analysis forhcoming. Diavaopoulos D. Doran J. Peerson D The informaion conen in implied idiosyncraic volailiy and he cross-secion of sock reurns: evidence from he opion markes. Journal of Fuures Markes Dimar R. Conrad J. Ghysels E kewness and he bubble. UNC working paper. 0

21 Doran J. Peerson D. Tarran B Is here informaion in he volailiy skew? Journal of Fuures Markes Heson A closed-form soluion of opions wih sochasic volailiy wih applicaions o bond and currency opions. Review of Financial udies Ho L.C.J Opion rading and he relaion beween price and earnings: a crosssecional analysis. Accouning Review Jennings R. arks L Earnings announcemens sock price adjusmen and he exisence of opion markes. Journal of Finance Landsman W.R. Maydew E.L. 00. Has he informaion conen of quarerly earnings announcemens declined in he pas hree decades? Journal of Accouning Research Manaser. Rendleman R.J. Jr Opion prices as predicors of equilibrium sock prices. Journal of Finance Mendenhall R. Fehrs D Opion lising and he sock-price response o earnings announcemens. Journal of Accouning and Economics Pan J. 00. The jump-risk premia implici in opions: evidence from an inegraed ime-series sudy. Journal of Financial Economics Paell J.M. Wolfson M.A The ex ane and ex pos price effecs of quarerly earnings announcemens refleced in opion and sock prices. Journal of Accouning Research Paell J.M. Wolfson M.A Anicipaed informaion releases refleced in call opion prices. Journal of Accouning and Economics heikh A.M. Ronn E.I A characerizaion of he daily and inraday behavior of reurns on opions. Journal of Finance kinner D.J Opions markes and he informaion conen of accouning earnings releases. Journal of Accouning and Economics Zhang X. Zhao R. Xing Y Wha does individual opion volailiy smirk ell us abou fuure equiy reurns? Journal of Financial and Quaniaive Analysis forhcoming. 1

22 Table 1: Descripive saisics for buy-and-hold reurn deciles over days 01 The sample is divided ino deciles based on buy-and-hold reurns BHRs over days 01. Day 0 is he earnings announcemen day. Mean values for BHRs and implied skewness kurosis and volailiy a days and -30 are repored. Panel A gives skewness kurosis and volailiy levels while Panel B repors changes in hese measures compared o day -30. kewness and kurosis are calculaed as in Bakshi apadia and Madan 003. * is significan a he 5% level and ** is significan a he 1% level. Panel A: Levels Buy and Hold Reurn 01 Decile Low High High-Low BHR ** kewness ** kewness ** kewness * kewness urosis ** urosis * urosis urosis Volailiy Volailiy Volailiy Volailiy Panel B: Changes Low High High-Low kewness Change ** kewness Change ** kewness Change * urosis Change ** urosis Change ** urosis Change * Volailiy Change Volailiy Change Volailiy Change

23 Table : Implied skewness and kurosis changes by opion expiraion Firms are divided ino quiniles monhly according o buy-and-hold reurns BHRs. In Panels A and B firms are divided according o BHRs over days -41 wih skewness and kurosis changes repored over days In Panels C and D firms are divided according o BHRs over days -91 wih skewness and kurosis changes repored over days In Panels E and F firms are divided according o BHRs over days -191 wih skewness and kurosis changes repored over days kewness and kurosis are calculaed as in Bakshi apadia and Madan 003. Resuls are repored separaely for opions wih he nex expiraion dae monh and he following expiraion dae monh +1. The difference of he absolue values of skewness and kurosis beween he mauriies is repored for each panel. * is significan a he 5% level and ** is significan a he 1% level. Panel A: Reurn -41 Quinile kewness Change Low 3 4 High ΔMonh Expiraion ΔMonh ABΔ-ABΔ Panel B: Reurn -41 Quinile urosis Change Low 3 4 High ΔMonh Expiraion ΔMonh ABΔ-ABΔ ** 0.446** 0.401** 0.406** 0.357** Panel C: Reurn -91 Quinile kewness Change Low 3 4 High ΔMonh Expiraion ΔMonh ABΔ-ABΔ Panel D: Reurn -91 Quinile urosis Change Low 3 4 High ΔMonh Expiraion ΔMonh ABΔ-ABΔ ** 0.96** 0.81** 0.33** 0.3** Panel E: Reurn -191 Quinile kewness Change Low 3 4 High ΔMonh Expiraion ΔMonh ABΔ-ABΔ Panel F: Reurn -191 Quinile urosis Change Low 3 4 High ΔMonh Expiraion ΔMonh ABΔ-ABΔ ** 0.137** 0.109** 0.19** 0.096* 3

24 Table 3: ock reurns following implied skewness and kurosis changes In Panel A B firms are divided ino quiniles monhly according o implied skewness kurosis changes over days and and equal-weighed buy-and hold reurns BHRs are examined over periods and -191 respecively. Day 0 is he earnings announcemen dae. Mean values over he sample period for daily BHRs and skewness and kurosis changes are presened. The differences for BHRs beween high and low quiniles are given wih -saisics in parenheses. kewness and kurosis are calculaed as in Bakshi apadia and Madan 003. Panel A: kewness kewness Change Days kewness Change Days kewness Change Days-30-0 Change Quinile BHR -41 kewness Change BHR -91 kewness Change BHR -191 kewness Change Low High High- Low Panel B: urosis urosis Change Days urosis Change Days urosis Change Days Change Quinile BHR -41 urosis Change BHR -91 urosis Change BHR -191 urosis Change Low High High- Low

25 Table 4: ock reurns following soring by volailiy and hen eiher implied skewness or kurosis changes Firms are divided ino quiniles monhly according o volailiy or volailiy changes and hen divided ino quiniles based on implied skewness Panel A or kurosis Panel B changes. Volailiy skewness and kurosis changes are measured over days and Volailiy levels are measured on days and -0. ubsequen equal-weighed porfolio buy-and-hold reurns BHRs are examined for he periods and -191 respecively. Day 0 is he earnings announcemen dae. Mean values for daily BHRs. The differences for BHRs beween high and low quiniles are repored wih -saisics in parenheses. kewness and kurosis are calculaed as in Bakshi apadia and Madan 003. Volailiy is calculaed as he moneyness weighed implied volailiy for opions where ATM opions receive he mos weigh. Panel A: kewness Change BHR -41 Volailiy Quinile -5 Volailiy Change Quinile Low 3 4 High Low 3 4 High kewness Change Quinile Low High High- Low BHR -91 Volailiy Quinile -10 Volailiy Change Quinile Low 3 4 High Low 3 4 High Low kewness Change Quinile High High- Low BHR -191 Volailiy Quinile -0 Volailiy Change Quinile Low 3 4 High Low 3 4 High Low kewness Change Quinile High High- Low

26 Panel B: urosis Change BHR -41 Volailiy Quinile -5 Volailiy Change Quinile Low 3 4 High Low 3 4 High Low urosis Change Quinile High High- Low BHR -91 Volailiy Quinile -10 Volailiy Change Quinile Low 3 4 High Low 3 4 High Low urosis Change Quinile High High- Low BHR -191 Volailiy Quinile -0 Volailiy Change Quinile Low 3 4 High Low 3 4 High Low urosis Change Quinile High High- Low

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