Florida Sae Universiy Libraries Elecronic Theses, Treaises and Disseraions The Graduae School 2008 Two Essays on he Predicive Abiliy of Implied Volailiy Consanine Diavaopoulos Follow his and addiional works a he FSU Digial Library. For more informaion, please conac lib-ir@fsu.edu
FLORIDA STATE UNIVERSITY COLLEGE OF BUSINESS TWO ESSAYS ON THE PREDICTIVE ABILITY OF IMPLIED VOLATILITY By Consanine Diavaopoulos A Disseraion submied o he Deparmen of Finance in parial fulfillmen of he requiremens for he degree of Docor of Philosophy Degree Awarded: Summer Semeser, 2008
The members of he Commiee approve he disseraion of Consanine Diavaopoulos defended on April 3, 2008. David Peerson Major Professor Thomas W. Zuehlke Ouside Commiee Member James Doran Commiee Member Gary Benesh Commiee Member Bruce Billings Commiee Member Approved: Caryn L. Beck-Dudley, Dean, College of Business The Office of Graduae Sudies has verified and approved he above named commiee members. ii
TABLE OF CONTENTS Lis of Tables..... iv Lis of Figures..... v Absrac... vi INTRODUCTION... 1 1. THE INFORMATION CONTENT IN IMPLIED VOLATILITY AND THE CROSS- SECTION OF STOCK RETURNS: EVIDENCE FROM THE OPTION MARKETS.. 10 2. OPTION MARKET EFFICIENCY AND EARNINGS ANNOUNCEMENTS.. 35 CONCLUSION.... 63 APPENDIX.... 65 REFERENCES.. 66 BIOGRAPHICAL SKETCH. 70 iii
LIST OF TABLES Table 1. Descripive Saisics of Opion Firm Sample.... 25 Table 2. Forecasing Fuure Realized Volailiy... 26 Table 3. Forecasing Firm Fuure Realized Volailiy wih Idiosyncraic Volailiy... 27 Table 4. Fama-MacBeh Esimaion wih All Available Socks... 28 Table 5. Fama-MacBeh Esimaion on Socks wih Opions... 29 Table 6. Mean Values of Firm Characerisics for Sored Porfolios... 30 Table 7. Idiosyncraic Porfolio Percenage Reurns.... 31 Table 8. Double-Sored High Minus Low Percenage Porfolio Reurns... 32 Table 9. Percenage of Posiive Earnings Announcemen Surprises 50 Table 10. Sock and Opion Reurns by IV Difference Quiniles..... 51 Table 11. Sock and Opion Reurns by BKM Difference Quiniles.... 53 Table 12. Sock and Opion Reurns by IV Difference Quiniles (Time Effecs). 55 Table 13. Sock and Opion Reurns by BKM Difference Quiniles (Time Effecs)... 57 Table 14. Reurns o Pu-Call Pariy Porfolios....... 59 Table 15. Reurns o Pu-Call Pariy Porfolios (Time Effecs).... 60 Table 16. Raw and Abnormal Sock and Opion Reurns. 61 Table 17. Raw and Abnormal Sock and Opion Reurns by Impled Volailiy Difference Quiniles..... 62 iv
LIST OF FIGURES Figure 1. Cumulaive Dollar Values for Implied and Realized Idiosyncraic Volailiy. 33 Figure 2. Small Size and High Book-o-Marke Equiy Cumulaive Dollar Values... 34 v
ABSTRACT This disseraion examines he informaion conen of implied volailiy wih regard o fuure asse reurns and fuure earnings announcemens. By definiion, implied volailiy is he marke s bes guess of he fuure volailiy over he erm of he opion. Thus, he objecive of my firs essay is o invesigae wheher expeced idiosyncraic risk (i.e. firm-specific risk as opposed o marke risk), as measured from implied volailiy, is relaed o fuure reurns. I find a srong posiive link beween implied idiosyncraic volailiy and fuure reurns. I is also clear ha hisorical realized idiosyncraic volailiy is unimporan in he presence of implied idiosyncraic volailiy. The robus resuls of my firs essay moivae he idea ha implied volailiy migh also conain informaion abou fuure earnings. Therefore, in my second essay I examine wheher informaion abou earnings announcemen surprises is imbedded in opion prices (via implied volailiy and he implied volailiy skew) prior o he announcemen. I find some limied suppor for his idea. In paricular, he resuls of my second essay sugges ha invesors migh profi by buying pu opions in low volailiy skew firms 3, 10, 20, or even 30 days before he earnings announcemen. vi
INTRODUCTION The firs chaper of my disseraion examines he relaion beween risk and reurn in he sock marke. This is a long sanding fundamenal issue in finance. Sandard asse pricing models such as he Sharpe-Linner (1964, 1965) capial asse pricing model (CAPM) and he Ross (1976) arbirage pricing heorem (APT) sugges a posiive relaion beween sysemaic risk and reurn, and many sudies es his heoreical predicion. Theoreically, sysemaic risk is he aspec of oal risk linked o reurns. A more recen srand of lieraure, however, suggess ha unsysemaic, or idiosyncraic, risk may be wha is acually driving his risk-reurn relaion. Many examine he cross-secional relaion beween equiy reurns and idiosyncraic risk. Douglas (1969), Linner (1965), and Lehmann (1990) find ha reurns are posiively relaed o marke model residuals. Meron (1987), Barberis and Huang (2001), Jones and Rhodes-Kropf (2003), and Malkiel and Xu (2006) develop asse pricing models esablishing ha reurns are a posiive funcion of idiosyncraic risk. The argumens of hese models generally cener on he failure by invesors o hold diversified porfolios and hese invesors requiring compensaion for he addiional risk. Malkiel and Xu empirically find a posiive link beween reurns and idiosyncraic risk, even in he presence of variables represening size, book-o-marke equiy, and liquidiy. Chua, Goh, and Zhang (2005) use an auoregressive model and Fu (2007) and Spiegel and Wang (2007) use EGARCH models o esimae expeced idiosyncraic volailiy. They all find ha expeced reurns are posiively relaed o expeced idiosyncraic volailiy. In conras, Ang, Hodrick, Xing, and Zhang (2006) find a negaive cross-secional relaion beween reurns and idiosyncraic risk. These resuls are robus o he inclusion of oher independen variables and differen marke condiions. Their resuls do no seem aribuable o exposure o aggregae volailiy risk. Ang, Hodrick, Xing, and Zhang noe ha heir findings are couner o he heoreical argumen ha invesors require addiional reurns for bearing unsysemaic risk and prior empirical findings of a posiive relaion beween reurns and idiosyncraic risk. The auhors aribue his discrepancy wih oher sudies o heir focusing and soring on firm-level idiosyncraic volailiy, somehing oher sudies fail o do. Bali and Cakici (2007), however, demonsrae here is no robus significan relaion beween idiosyncraic volailiy and he cross-secion of expeced sock reurns. I is possible ha he puzzling resuls of Ang, Hodrick, Xing, and Zhang (2006) are due
o limis o arbirage or shor sale consrains. Miller (1977) posis ha large consrains on shor selling may lead o lower fuure reurns. Boehme, Danielsen, Kumar, and Sorescu (2005) and Duan, Hu, and McLean (2007) find shor ineres raios are linked o he relaion beween reurns and idiosyncraic risk. Duan, Hu, and McLean find a negaive relaion for he 5% of socks wih he highes shor ineres, bu no relaion for he remaining socks. Boehme, Danielsen, Kumar, and Sorescu use opion lising and shor ineres as measures of shor sale consrains. Socks wih (wihou) raded opions and wih low (high) shor ineres have low (high) shor sale consrains. They find a posiive (negaive) relaion beween reurns and idiosyncraic risk for socks wih low (high) shor sale consrains. There is no relaion beween reurns and idiosyncraic risk for he enire opion sample and he enire non-opion sample. Baalio and Schulz (2006) do no find any evidence of shor sales resricions for Inerne socks early in he year 2000. This is imporan because i provides evidence of an absence of shor sales resricions for socks underlying acively raded opions. By examining a broad specrum of socks from he NYSE, AMEX, and Nasdaq, Ang Hodrick, Xing, and Zhang (2006) are likely mixing many securiies wih limis o arbirage and shor sale consrains along wih oher securiies wihou hese limis and consrains. This may affec heir finding of a negaive relaion beween sock reurns and idiosyncraic risk. Therefore, in he spiri of Boehme, Danielsen, Kumar, and Sorescu (2005) and Baalio and Schulz, I examine he effec of shor sale consrains and idiosyncraic volailiy on sock reurns. The naure of he cross-secional relaion beween idiosyncraic risk and reurns is currenly unclear. One weakness wih prior sudies is he use of hisorical risk measures. Since ex-ane marke expecaions likely provide beer assessmens for fuure volailiy han pas volailiy, I examine he relaion beween expeced volailiy and fuure reurns. Thus, my analysis is similar in spiri o ha in Chua, Goh, and Zhang (2005), Fu (2007), and Spiegel and Wang (2007). I do no, however, employ realized idiosyncraic volailiy and a saisical model o esimae expeced idiosyncraic volailiy. Insead, we direcly assess expeced volailiy as he implied volailiy from observed opion prices. From his measure I hen derive implied idiosyncraic volailiy. By definiion, implied volailiy is he marke s bes guess of he fuure volailiy over he erm of he opion. Consequenly, he predicive power of implied volailiy is examined in muliple sudies. For example, Chrisensen and Prabhala (1998) find ha he volailiy implied 2
by S&P 100 index opion prices ouperforms pas volailiy in forecasing fuure index volailiy. Doran and Ronn (2006) noe ha his esimae is biased and may be relaed o he volailiy risk premium. Oher sudies examine he predicive abiliy of he CBOE volailiy index, VIX, for sock reurns. 1 Gio (2005) finds ha VIX is useful for predicing reurns on he S&P 100. Copeland and Copeland (1999) deermine ha VIX levels predic reurns on various indices formed on size and growh versus value characerisics. Banerjee, Doran, and Peerson (2007) find ha VIX levels and innovaions predic he reurns of characerisic based porfolios. I use a forward looking measure of idiosyncraic volailiy and examine is cross-secional relaion o firm-level fuure reurns. Thus, he objecive of my sudy is o invesigae wheher expeced idiosyncraic risk, as measured from implied volailiy, is relaed o fuure reurns. I also examine if he predicive abiliy of implied idiosyncraic risk is sronger han ha of realized idiosyncraic volailiy and forecass of volailiy from saisical models. Using sock and opion prices for all firms wih raded opions, I calculae measures of implied and realized idiosyncraic volailiy. I also calculae idiosyncraic volailiy forecass from EGARCH and auoregressive models. I find ha implied idiosyncraic volailiy srongly predics realized volailiy a he firm level, and he effec is greaer han ha from pas realized idiosyncraic volailiy or volailiy forecass from saisical models. Nex, using a Fama and MacBeh (1973) cross-secional analysis and conrolling for firm-specific effecs, I show ha implied idiosyncraic volailiy posiively predics fuure sock reurns, bu pas realized idiosyncraic volailiy is unrelaed o fuure reurns. Idiosyncraic volailiy forecased from saisical models is no significanly relaed o reurns when implied idiosyncraic volailiy is included as an explanaory variable. Finally, I sor my sample by implied and realized idiosyncraic volailiies and examine porfolio reurns. I use boh equal and value weigh he porfolios. I consisenly find ha implied idiosyncraic volailiy is more closely linked o fuure reurns han realized idiosyncraic volailiy. I direcly compare he fuure reurn forecasing power for implied idiosyncraic and pas realized volailiies. Implied idiosyncraic volailiy has a srong, posiive forecasing power for fuure reurns when realized idiosyncraic volailiy is conrolled for. However, realized idiosyncraic volailiy has no significan forecasing power when implied idiosyncraic volailiy 1 VIX is a measure of marke expecaions of sock index reurn volailiy over he nex 30 calendar days. Beginning in 2003, VIX is calculaed from he S&P 500 index opion prices. The calculaion is based on a wide range of srike prices and is independen of any opion pricing model. 3
is conrolled for. The relaion is sronges for small firms and high book-o-marke equiy firms. While I presen high alphas, I sugges an alernaive explanaion ha idiosyncraic risk should be a priced facor in asse pricing models. The second chaper of my disseraion examines wheher informaion abou earnings announcemen surprises is imbedded in opion prices prior o he announcemen. Much work has been done on pos-earnings-announcemen drif (PEAD) 2, and PEAD appears o be an enduring feaure of sock reurns. 3 However, he exising lieraure seems o be more concerned wih he differences in sock reurns beween opion and non-opion firms, raher han he differences in reurns o various opion based sraegies formed around earnings announcemens. In paricular, Jennings and Sarks (1986) examine he sock price adjusmen o he release of quarerly earnings using samples of firms wih and wihou lised opions. They find he wo samples exhibi differen adjusmen processes, wih he non-opion firms requiring subsanially more ime o adjus. Their findings are consisen wih he hypohesis ha he common sock of firms wih exchange lised opions is associaed wih a differen price adjusmen process han ha of non-opion firms. Overall, he Jennings and Sarks (1986) resuls suppor he argumen ha opion markes are useful in disseminaing earnings news and improving marke efficiency. Along similar lines, Skinner (1990) examines wheher a firm s lising on an opions exchange is associaed wih changes in he informaion conen of is accouning earnings releases. For he majoriy of firms in he sudy, he size of he sock-price reacion o accouning earnings releases is smaller afer exchange-raded opions are lised on he respecive socks. Skinner argues ha his evidence is consisen wih he view ha opions lising improves he informaional efficiency of he marke for he underlying sock. One inerpreaion of his evidence is ha opions lising causes hese firms o be more closely followed afer opions lising, hus reducing he poenial informaion conen of heir public informaion releases. The auhor poins ou, however, ha i is difficul o draw causal inferences since he incenives of he opions exchanges make i unlikely ha hey selec socks randomly. Therefore, i is plausible ha he observed changes in informaional efficiency are simply a funcion of he way ha opions exchanges choose socks, raher han reflecing he informaional effecs of opions rading iself. 2 Pos-earnings-announcemen drif is he endency for a sock s price o drif in he direcion of an earnings surprise following an earnings announcemen. 3 See Foser, Olsen, Shevlin (1984), Bernard and Thomas (1989, 1990), and Freeman and Tse (1989). 4
Ho (1993) essenially exends and complemens he work of Skinner (1990) and Jennings and Sarks (1986). She documens differences in he price-earnings relaion beween firms wih and wihou lised opions. In paricular, she finds ha he surprise associaed wih quarerly earnings announcemens is greaer for non-opion firms han for opion firms, and ha he securiy prices of opion firms anicipae earnings changes earlier han hose of non-opion firms. However, she is careful o conclude ha her resuls simply sugges an associaion beween opion rading and reurn behavior in conjuncion wih earnings announcemens. Mendenhall and Fehrs (1999) reexamine he issue of he effec of opion lising on he sock-price response o earnings announcemens. Their analysis exends prior sudies by examining a more recen ime period and by considering addiional facors. They aemp o conrol for changing marke condiions ha end o affec he earnings response of all firms (no jus hose lising opions) and o correc for firm size. Their resuls sugges ha boh of hese facors may be imporan. However, conrary o prior sudies using earlier daa, hey find ha firms iniiaing opion rading afer 1986 fail o exhibi a significan decline in he response rae o earnings surprises. In fac, hey find evidence ha opion lising may acually increase he sock-price response rae o earnings, bu no evidence ha lising reduces he response rae. A possible explanaion for his las resul is posied by he auhors. They argue ha if informed raders can ake larger and less expensive posiions in opion firms han hey can in non-opion firms, and if he oal response o earnings is no complee for several monhs following he announcemen, hen heir resuls migh represen a more complee announcemen-day response for opion firms ha is caused by he acions of informed raders. Thus, heir resuls, hough differen, migh sill imply ha opion lising increases sock marke efficiency. However, Mendenhall (2004) believes ha PEAD is aribuable o invesors who underreac o earnings surprises and arbirage does no eliminae he drif because he required rades are risky. In fac, he conrols for a wide range of firm-specific characerisics and finds ha he magniude of PEAD is significanly posiively relaed o he risk faced by an arbirageur who akes a posiion in he mispriced sock and ries o hedge he posiion using various marke indexes. He also finds some evidence ha he magniude of he drif is posiively relaed o ransacions coss and concludes ha hese resuls represen new evidence ha PEAD reflecs underreacion o earnings informaion and ha arbirage risk and ransacions coss impede arbirageurs who aemp o profi from i. 5
Finally, Baallio and Mendenhall (2005) consider earnings expecaions and he reurn relaionship o invesor rade size. They find ha smaller, less sophisicaed invesors ignore earnings signals based on analyss forecass and respond o signals of a less accurae ime-series model. Large raders, on he oher hand, use a more complee informaion se ha incorporaes ime-series signals along wih oher informaion refleced in analyss forecass. They conclude, as hypohesized by Bernard and Thomas (1990), ha he acions of hese smaller unsophisicaed invesors is wha gives rise o PEAD. One limiaion of he previous research discussed is ha i does no invesigae rading on opions markes. Insead, i focuses on changes in he marke for he underlying sock. On he oher hand, Amin and Lee (1997) examine rading behavior on boh he opions and sock markes around he ime of earnings announcemens. They 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%. 4 Ineresingly, hey show ha he direcion of his preannouncemen rading in opions foreshadows subsequen earnings news. Specifically, hey 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. This poin is made by Black (1975), who argues ha raders wih privae informaion prefer o exploi ha informaion by rading on he opions marke. He argues ha opions markes provide lower shor selling coss and higher leverage, and ha many poenial informaion raders will rade on he opions marke when hey wouldn boher o rade a all if he opions marke didn exis. A large amoun of research has invesigaed he links beween opions and equiy markes, bu he evidence is inconclusive as o which of he wo markes reflecs new informaion earlier. Early suppor for Black s argumens is found by Manaser and Rendelman (1982) who posi ha opion markes may provide a preferred oule for informed invesors. They find ha he closing prices of lised call opions conain informaion abou equilibrium sock prices ha is no conained in he closing prices of underlying socks. They offer wo poenial explanaions for heir finding. The simples is ha closing opion and sock ransacions do no always ake place a he same ime. The alernaive is ha closing opion 4 Abnormal rading volume is measured as he percenage deviaion from he daily mean for each firm and averaged across all firms. Their resuls for opions (socks) are saisically significan (insignifican) a he 5% level. 6
prices reflec fundamenal informaion abou he equilibrium values of underlying socks ha is no conained in closing sock prices. To es his hey use he Black and Scholes (1973) opion pricing model o calculae implied sock prices o compare wih observed sock prices 24 hours laer. They wai 24 hours o allow ime for he nonsynchronous daa effec o be absorbed ino observed sock prices. However, heir analysis reveals ha he implied prices sill conain informaion regarding equilibrium sock prices ha is no fully refleced in observed sock prices a day laer. Thus, hey conclude ha opion prices do reflec informaion no already presen in sock prices. Sheikh and Ronn (1994) examine opion reurn paerns, and argue ha differences beween hese and equiy marke reurns are evidence of informaion based rades in opions. In paricular hey 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. Easley, O Hara, and Srinivas (1998) invesigae he informaional role of ransacions volume in opions markes by developing and esing an asymmeric informaion model in which informed raders may rade in opion or equiy markes. Their main empirical resul is ha negaive and posiive opion volumes conain informaion abou fuure sock prices. In paricular, hey find ha cerain opion volumes lead sock price changes, hus supporing he noion ha opions markes are an imporan venue for informaion based rading. Overall, i appears ha many sudies are more concerned abou he earnings announcemen iself, raher han he effec on he opions marke. Bu a slow reacion o a surprise in he earnings announcemen is an inefficiency in he marke. One of he moivaions for his sudy sems from findings in previous research ha opion lising and subsequen rading do increase available informaion, and hence marke efficiency. Therefore, in his essay I examine how he opions marke iself anicipaes his poenial inefficiency and wheher raders can profi from i. My hypohesis is ha informaion abou earnings announcemen surprises is imbedded in opion prices prior o he announcemen. I also hypohesize ha his informaion is refleced in opion prices before i is refleced in sock prices, he laer of which may no be unil he acual 7
announcemen. 5 Because of he greaer leverage, I expec informed raders o rade ou-of-hemoney opions firs. To es his idea, I begin by using he implied volailiy skew o predic earnings per share announcemen surprises. 6 The findings of Doran, Peerson, and Tarran (2007) sugges ha here is predicive informaion conen wihin he volailiy skew, especially in he shor erm. In paricular hey find ha in he shor-erm he pu volailiy skew has srong predicive power in forecasing marke declines while he call skew has some power in predicing upward marke spikes. Therefore, I use he call volailiy skew o anicipae good news and he pu volailiy skew o anicipae bad news. Informaion should be refleced in he ou-of-hemoney (OTM) implied volailiies being high relaive o he in-he-money (ITM) implied volailiies. I also check if he volailiy skew is relaed o sandardized unexpeced earnings. I expec ha i is, bu poin ou ha I can sill exploi he informaion in he volailiy skew even if he relaion beween earnings surprise and he volailiy skew does no urn ou o be wha I anicipae. 7 Based on he volailiy skew, I examine wo differen ypes of rading sraegies. Each sraegy focuses on firms in he exreme skew quiniles. Firs, I compare sock reurns wih opion reurns. I consider raw and abnormal reurns o a buy and hold sraegy for sock and opions hrough he earnings announcemen and compare hese reurns across groups of firms in he high and low volailiy skew quiniles. If a higher implied volailiy skew means ha opion prices have already adjused in expecaion of an earnings surprise bu he sock has no, hen he 5 In paricular, I idenify wo ypes of forces ha allow sock prices o adjus ha I assume are no working. Firs, he earnings informaion iself. Tha is, if he sock marke anicipaed earnings informaion he way he opions marke does, hen sock prices should also adjus. Therefore, he sock marke is no efficienly responding o he informaion abou earnings ha he opions marke hinks i knows. Second, even if sock holders know nohing abou earnings, hey can sill see opion prices moving. Therefore, i is expeced ha invesors would iniiae rades using he pu-call pariy relaion beween socks and opions o help bring sock prices ino line. However, even hough he pu-call pariy relaion would normally be expeced o cause sock prices o change when opion prices change, we are assuming he mechanism is no fully working. Firs, 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 more freedom in he relaionship beween prices of socks and opions. Second, invesors who ry o exploi he relaionship 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. 6 Implied volailiy is he volailiy implied from an opion price using he Black-Scholes or a similar model. The implied volailiy skew is implied volailiy ploed agains increasing srike prices for a group of opions wih he same expiraion dae. 7 If he implied volailiy skew is no relaed o SUEs, hen an opion rading sraegy is suggesed wih long (shor) posiions for in (ou of) he money opions. 8
sock posiion should subsequenly ouperform an equivalen posiion in opions. To examine his I compare abnormal reurns o sock and opion posiions using he opion s bea o consruc our abnormal reurn measure for he opion posiion. Second, I form zero-cos porfolios of opions and sock for firms based on he pu-call pariy relaionship. Tha is, sock values are expressed as a funcion of opion values. My hypohesis is ha he opions marke anicipaes he earnings surprise, and hence, a poenial arbirage profi can be capured by forming a hese porfolios. Specifically, we shor he sock and shor a pu on he sock in he days before he earnings announcemen and use he proceeds o purchase a call on he sock and inves he remaining cash a he risk free rae. The posiion is hen closed he day afer he earnings announcemen. If he opions marke anicipaes he direcion of he earnings surprise, and if he sock marke does no anicipae he surprise, hen invesors should be able o make money wih his sraegy. I examine he profis o my zero-cos arbirage porfolios from he ime I sor socks ino quiniles based on he volailiy skew, hrough he announcemen dae. Again, if he opions marke reflecs informaion abou upcoming SUEs ha he sock marke does no ye incorporae, hen my arbirage porfolios should earn posiive profis. However, even hough here may be informaion in he opions marke ha is no in he sock marke, i is possible ha my zero-cos porfolios do no generae abnormal reurns because of he consrain of pu-call pariy or he bid-ask spread. If I do no find abnormal reurns o my zero-cos porfolios, hen his suggess ha even hough opion prices may have already adjused in expecaion of an earnings surprise, i canno be aken advanage of. Overall, I find limied suppor for my hypohesis and he resuls of my second essay sugges ha invesors migh profi by buying pu opions in low volailiy skew firms 3, 10, 20, or even 30 days before he earnings announcemen. 9
CHAPTER 1 THE INFORMATION CONTENT IN IMPLIED VOLATILITY AND THE CROSS-SECTION OF STOCK RETURNS: EVIDENCE FROM THE OPTION MARKETS Daa Descripion and Measures of Volailiy I employ individual company daily implied reurn volailiy daa, from January 1996 hrough June 2005, made available from OpionMerics. 8 Opion open ineres is also provided by OpionMerics. I obain sock reurns, share prices, and number of shares ousanding from CRSP and book value of equiy from Compussa. 9 The CRSP and Compusa daa I obain is no resriced o solely firms wih opions or o he period 1996-2005. Daily reurns for he hree Fama and French (1993) facors (MKT, SMB, HML) and he Carhar (1997) momenum facor (UMD) are obained from Kenneh French s websie. For he opion sample I use all firms wih raded opions wih he condiion ha here is a leas five years of prior sock reurn daa. This is necessary for he calculaion of he firm s bea and he calculaion of idiosyncraic implied and realized volailiy. To calculae firm j s bea, monhly firm reurns, r, are regressed on marke reurns using he prior 60 monhs: r = j + β jmret + e α (1) where MRET is he reurn on he CRSP value-weighed index. Each subsequen monh he sample is updaed o use only he prior 60 monhs, giving a rolling bea esimae for each firm. 10 8 OpionMerics is a financial research and consuling firm specializing in economeric analysis of opions markes. 9 We exclude all ETFs and foreign, financial, and uiliy socks. We include only firms wih a 10 or 11 share code. 10 To check for he robusness of our bea calculaion, we use he Fama and French (1993) hree-facor model marke bea and a porfolio bea. The porfolio bea is calculaed in a similar fashion o Fama and French (1992) and Fu (2007) by forming a rolling monhly esimaion of equal-weighed reurns for 10x10 porfolios based on size and firm beas. These porfolio reurns are hen regressed on he curren and one-monh lagged value-weighed index reurns o generae porfolio beas, which are assigned o he individual firms depending on heir size and bea decile. The subsequen calculaion of 2 σ IV _ idio, using eiher he Fama and French (1993) hree-facor model marke bea or he porfolio bea have correlaions wih he marke model bea of.83 and.72, respecively. There is no qualiaive impac on he predicive power of implied idiosyncraic volailiy o forecas fuure idiosyncraic realized volailiy and reurns using eiher alernaive bea calculaion. The resuls are available upon reques. 10
For each firm wihin he opion sample, he opion implied volailiies are calculaed by OpionMerics using American or European models where appropriae. Since here are a variey of srike prices and mauriies for each firm on a given day, a sandardized implied volailiy is calculaed by employing he mos weigh on implied volailiies wih a-he-money opions closes o 30 days o mauriy for boh calls and pus. Averaging across all opions reduces he measuremen error associaed wih invering opion prices o obain implied volailiies. 11 To calculae he idiosyncraic porion of implied volailiy, I express implied marke volailiy as a funcion of marke volailiy, in a fashion similar o Dennis, Mayhew, and Sivers (2006), such ha: σ = β σ + σ (2) 2 2 2 2 IV, j IV _ M, IV _ idio, σ IV _ M, 2 2 where is he implied marke variance from VIX on day, is he implied oal 2 variance for firm j a ime, is he squared marke bea from he esimaion of equaion (1), σ IV _ idio, β j σ IV, j, 2 and is he idiosyncraic porion of implied variance for firm j a ime. My measure of implied idiosyncraic volailiy is he square roo of he idiosyncraic porion of implied variance. Theoreically, his value should no be less han or equal o zero, bu empirically i is possible. A small number of hem have non-posiive values and I se hese equal o zero. I creae one monh annualized realized volailiy as he annualized sandard deviaion of daily reurns wihin he given monh for each firm. To exrac he realized idiosyncraic porion, reurns of he individual firms are regressed on marke reurns using equaion (1), bu wih a daily frequency. To creae he realized idiosyncraic risk measure, σ deviaions of he daily residuals are calculaed for he given monh as: ( ) 2 e e RV _ idio,, he sandard N 1 σ RV _ idio, =, n (3) N = n 1 where N equals he number of days in he given monh, e j,, n is he residual for firm j on day n in monh, and e j, is he mean residual for firm j over he N days in monh. This sandard deviaion measure is hen annualized. 11 See Henschel (2003) for deails. 11
To compare he forecas power of implied idiosyncraic volailiy relaive o realized idiosyncraic volailiy, I also consruc wo saisical forecass of realized idiosyncraic volailiy. The firs is from he Nelson (1991) EGARCH (p,q) model, as used in Fu (2007) and Spiegel and Wang (2007). The benefi of he EGARCH versus he GARCH model is ha is does no require resricing he parameers o insure a non-negaive variance. The funcion form is: R = α + β MKT + β SMB + β HML + ε, 2 ~ N(0, σ j 1, j M, 2, j 3, j ε ) (4) lnσ ε ε π (5) φ p q 2 2 k k EG _ idio, = ai + b lnσ 1 + c Φ θ + γ 2/ φ = 1 Φ= 1 σ k σ k where he monhly reurns are described in he hree-facor model in equaion (4), and he 2 condiional variance for firm, is a funcion of he pas p residual variances and q- σ EG _ idio, i, period reurn shocks. Equaions (4) and (5) are esimaed for each sock using a leas 60 monhly reurns. The square roo of he condiional variance is he measure of idiosyncraic volailiy. The second saisical forecas uses a 2 nd order auoregressive model, AR(2), o esimae idiosyncraic volailiy, similar o ha of Chua, Goh, and Zhang (2005). Using he squared residual from equaion (4), idiosyncraic variance for firm j is expressed as: σ ϑ ϑ ε ϑ ε + η 2 2 2 AR _ idio, = 1, j + 2, j 1 + 3, j 2 (6) An AR(2) is preferred o an AR(1) process since he laer ends o have high serial correlaion. My measure of idiosyncraic volailiy is he square roo of he idiosyncraic variance. Two addiional conrols are included o accoun for possible liquidiy issues or shor-sale consrains. They reflec my focus on firms wih raded opions. Highly liquid socks are less likely o have marke fricions. My measure of liquidiy, OI, is defined as he log of opion open ineres plus one, where open ineres is aggregaed across all opions for a firm. I employ he shor-sale consrain measure defined in Ofek, Richardson, and Whielaw (2004) as: ORW_Raio S 100 * ln S = * (7) 12
where S is he curren sock price, and S * is he heoreical sock price calculaed from he pucall pariy relaion which includes he early exercise premium on he pu. 12 If here is a shorsale consrain, he ORW_Raio should exceed zero. The inclusion of hese conrols is designed o es he hypohesis ha firms ha have higher liquidiy and/or lower shor-sale consrains may have differen price responses o volailiy han hose firms ha are more consrained. Descripive Saisics Table 1 provides descripive saisics for he opion sample over he period 1996 hrough June 2005. Daa is averaged across ime for an individual firm, and hen descripive saisics across firms are presened. The oal number of monhly firm observaions is 132,634, wih a oal of 2,253 unique firms. On average here are 1704 firms in any given monh and he average firm wihin he sample has 75 observaions. Marke value of equiy (SIZE) is measured a he end of each monh. The cross-secional average, median, and 5 h and 95 h percenile values for firm size correspond very closely o he Fama and French (1993) perceniles. Book-o-marke equiy (B/M), calculaed for a given monh in calendar year, is compued using he end of prior monh marke value of equiy and book equiy from fiscal year -2. This insures ha equiy values are known a he ime hey are used. The B/M values are slighly lower han Fama and French values in each caegory, wih he median and 95 h percenile values equal o he 40 h percenile and 85 h percenile values in Fama and French. Bea is calculaed from equaion (1) using he prior 60 monhs of reurns. The median bea is 1.03, and he 5 h and 95 h percenile values are 0.27 and 2.66, respecively. The disribuion of values for he shor-sale consrain (ORW_Raio) is similar o ha in he Ofek, Richardson, and Whielaw (2004) sample. So while he number of firms in my sample is significanly less han he full universe of available socks, based on he opion firm characerisics he sample is very represenaive. The cross-secional average and median firm implied volailiy is higher han he firm realized volailiy counerpars. This is similar o he marke relaion beween implied volailiy and realized volailiy, where he VIX index average volailiy over he period is 23.6% and he realized volailiy on he S&P 500 is 16.8%. These differences are significan a he 1% level for boh he marke and firm level. As Doran and Ronn (2006) poin ou, differences in implied and 12 Refer o equaion (3) in Ofek, Richardson, and Whielaw (2004). 13
realized marke volailiy may be a direc resul of a volailiy risk premium, which has a significan impac on he value of he underlying opions. Given ha his paern persiss a he firm level, i is possible ha he volailiy premium influences firm level opion prices as well. By comparing he means and medians, he idiosyncraic porion of realized oal volailiy is abou 80% percen. This is slighly lower han he 85% found by Goyal and Sana-Clara (2003), bu he idiosyncraic porion sill makes up he majoriy of realized volailiy. The mean and median implied idiosyncraic volailiy are similar o he realized and wo saisical forecas idiosyncraic volailiy measures, and make up abou 70% percen of implied oal volailiy. So while implied idiosyncraic volailiy accouns for a lower porion of implied oal volailiy han realized idiosyncraic volailiy does for realized oal volailiy, i is clearly he significan componen of implied oal volailiy. This is imporan given he relaion of implied and fuure realized volailiy and reurns. If mos of he implied volailiy is idiosyncraic, a he firm level he idiosyncraic porion may be a srong predicive componen. Mehodology and Resuls for Securiy-Level Analysis Predicive Power of Implied Volailiy To es for he informaion conen in implied volailiy in he opion sample, I firs examine he predicive power in forecasing fuure realized volailiy. I use monhly daa, observing he implied and realized volailiy on he las day of each monh, where realized volailiy is measured over he monh. This is done a he marke and individual firm levels as: σ RV _ M, + 1 = α + ξ1σ IV _ M, + ξ2σ RV _ M, + ε + 1 (8) RV, + 1 = α j + ξ1, jσ IV, + ξ 2, jσ RV, + ε + 1 σ (9) where σ RV _ M, is he annualized realized monhly volailiy on he S&P 500 in monh and σ IV _ M, is he VIX index in monh. ε denoes a residual, and α andξ represen coefficiens o be esimaed. Equaion (8) is he regression specificaion for he marke. Equaion (9) is he regression specificaion for he individual firm j. In each case his is a es of he informaion conen in oal implied volailiy, and he samples have non-overlapping observaions. For he 14
firm level regressions, each firm s coefficiens are esimaed separaely and hen mean and median coefficiens across firms are presened, along wih he proporion significan a he 5% level. In a reverse Fama and MacBeh (1973) mehodology, -saisics are formed from he cross-secional disribuion of he firm coefficiens. I require a leas 60 observaions for he firm o be included, reducing he sample o 1310 firms. I presen he resuls in Table 2. Panel A repors he coefficien esimaes and -saisics (in parenheses) for he marke regression, wih and wihou he resricion ha ξ = 2 0. The coefficiens on implied marke volailiy are posiive and significan a he 1% level, while he coefficien on realized marke volailiy is insignifican. Consisen wih Chrisiansen and Prabhala (1998) and ohers, implied volailiy is he efficien predicor of fuure realized volailiy, even in he presence of pas realized volailiy. From column one, a es for ξ = 1 1 reveals a -saisic of 3.49 (no shown), suggesing ha ξ 1 is significanly differen from one. Thus, implied volailiy is an upward biased predicor of fuure realized volailiy. This suggess a srong volailiy risk premium. Panel B repors he firm-level resuls. Mean and median (across firm) coefficiens are presened, in brackes are he 25 h and 75 h percenile values, and in parenheses are he reverse Fama and MacBeh (1973) -saisics. Firm-level resuls are similar o he marke-level resuls. When pas realized volailiy is included, firm implied volailiy is sill he efficien predicor of fuure realized volailiy. This is differen from prior findings, such as hose by Bakshi and Kapadia (2003) and Dennis, Mayhew, and Sivers (2006), showing ha oal implied volailiy is an unbiased and efficien esimaor of oal realized volailiy. These sudies use daa from a small sample of firms and employ he 1988-1995 ime period, which had very low volailiy. The conclusions in Bakshi and Kapadia and Dennis, Mayhew, and Sivers a he firm level are consisen wih he conclusion in Chrisensen and Prabhala (1998) for he marke level. However, I now know ha he Chrisensen and Prabhala resuls are a funcion of he ime period, and do no hold generally. My findings a he firm level are consisen wih new evidence, as in Doran and Ronn (2006), showing implied volailiy is an upward biased predicor of fuure realized volailiy a he marke level. Predicive Power of Implied Idiosyncraic Volailiy 15
Nex, for he opion sample I compare he forecasing abiliy of implied idiosyncraic volailiy, saisical forecass from he EGARCH and AR(2) models, and hisorical realized volailiy, as predicors for fuure realized idiosyncraic volailiy. I observe hisorical realized idiosyncraic volailiy for monh, implied idiosyncraic volailiy a he end of monh ha is a forecas for monh +1, and forecass of monh +1 idiosyncraic volailiy from EGARCH and AR(2) models using daa hrough monh. For each firm j I regress fuure realized idiosyncraic volailiy on he forecased measures as: σ α ψ σ ψ σ ψ σ ψ σ ε (10) RV _ idio, + 1 = j + 1, j IV _ idio, + 2, j EG _ idio, + 3, j AR _ idio, + 4, j RV _ idio, + + 1 where α and ψ s are esimaed coefficiens. Similar o he regression resuls repored in Panel B of Table 2, coefficiens for each firm are esimaed separaely, wih mean and median coefficiens presened along wih heir 25 h and 75 h percenile values. I also presen -saisics from he reverse Fama-MacBeh procedure. I show he resuls in Table 3 wih he same forma as Panel B of Table 2. They are presened for he full model in equaion (10) as well as resriced subses. The sample size drops from Table 2 because I lack sufficien daa o calculae bea for some firms; bea is needed so I can calculae implied idiosyncraic volailiy. The firs column in Table 3 shows ha boh implied and hisorical realized idiosyncraic volailiy are posiively relaed o fuure idiosyncraic volailiy, bu he relaion is sronger for implied volailiy wih a significan -saisic from he Fama-MacBeh regressions. The second and hird columns show ha hisorical realized idiosyncraic volailiy is a sronger predicor of fuure volailiy han each of he saisical models; only hisorical volailiy has a significan - saisic. Finally, he las column includes all four idiosyncraic volailiy forecas measures. Implied idiosyncraic volailiy has he sronges relaion wih fuure idiosyncraic volailiy and i is he only measure wih a significan Fama-MacBeh -saisic. Thus, implied idiosyncraic volailiy dominaes he oher measures as a predicor of fuure idiosyncraic volailiy. Fama-MacBeh Fuure Reurn Esimaion To es he relaion beween firm fuure reurns and idiosyncraic risk, I firs revisi he sample and resuls presened in Ang, Hodrick, Xing, and Zhang (2006). They find a negaive correlaion beween fuure reurns and hisorical realized idiosyncraic volailiy. They do no, however, examine relaions a he firm level or conrol for firm characerisics. I esimae a he 16
firm level and on a monhly basis he relaion beween fuure reurns and hisorical idiosyncraic volailiy, using Fama and MacBeh (1973) regressions and firm-specific conrols: r + 1 = α + λ1σ RV _ idio, + λ2 LSIZE + λ3lbm + λ4r λ λ λ β ε (11) + 5 r 11: 1 + 6r 35: 12 + 7 + + 1 where r j is he reurn for sock LSIZE is he log of marke equiy, and LBM is he log of booko-marke equiy. Boh are measured a he end of he monh and book-o-marke equiy is calculaed as defined previously. The hree reurns ha are independen variables precede he dependen variable reurn by one monh, he eleven monhs prior o he firs reurn independen variable, and he 24 monhs prior o he second independen reurn variable, respecively. α and λ s are coefficiens o be esimaed. The cross-secional regressions are esimaed wih and wihou he firm characerisic conrols, and over wo separae ime periods. The firs is he same ime period used in Ang e al., 1963-2000. The second is from 1996 hrough June 2005 and corresponds o he period of my opions daa. For boh periods I use all available firms and do no confine he analysis o firms wih raded opions. I presen he resuls in Table 4. 13 The resuls for he Ang e al. (2006) ime period show a negaive bu insignifican coefficien on realized idiosyncraic volailiy. This holds regardless of wheher he firm conrols are included or no. The direcion of he coefficien sign is consisen wih heir findings, bu he lack of saisical significance is roubling. The resuls for he period 1996 hrough June 2005 also show no imporan role for realized idiosyncraic volailiy. Wihou he firm conrols, he coefficien on realized idiosyncraic volailiy has a posiive, insignifican sign. Wih firm conrols, he coefficien sign is negaive bu i is sill insignifican. From he resuls in Table 4 here is lile I can conclude abou he relaion beween idiosyncraic realized volailiy and fuure reurns. This is consisen wih he findings in Bali and Cakici (2007). Using socks wih raded opions, I examine he relaion beween implied idiosyncraic risk and fuure reurns. The esimaion period is 1996 hrough June 2005. Equaion (11) is modified o include implied idiosyncraic volailiy, he saisical idiosyncraic volailiy forecass, he shor sale consrain, ORW_Raio, and he log of monhly open ineres, OI: 13 In an earlier version of his paper we included he macro facors dividend-price raio, relaive Treasury bill rae, erm spread, and defaul spread, along wih implied idiosyncraic volailiy, o examine he ime-series properies of each individual firm. Implied idiosyncraic volailiy reained a posiive and significan effec on fuure reurns. 17
r + 1 = α + λ σ 1 + λ β 7 RV _ idio, + λ σ 8 + λ LSIZE 2 IV _ idio, + λ σ 9 + λ LBM 3 EG _ idio, + λ r + λ σ 10 4 + λ r AR _ idio, 5 11: 1 + λ ORW 11 + λ r 6 35: 12 λ ε _ Raio + 12OI + + 1 (12) In Table 5 I presen he esimaion resuls from various combinaions of independen variables from equaion (12), using he Fama and MacBeh (1973) mehodology. 14 The resuls demonsrae a srong posiive and significan relaion beween implied idiosyncraic volailiy and fuure reurns; coefficiens are significan a he 1% level regardless of he specificaion or sample. In conras, he coefficiens on realized idiosyncraic volailiy are insignifican in all specificaions. The coefficiens on he saisical forecass from he EGARCH and AR(2) models are posiive and significan when he respecive variables are individually combined wih realized idiosyncraic volailiy. However, when all four idiosyncraic volailiy measures are included ogeher, he only significan coefficien is for implied volailiy. The coefficiens for size, book-o-marke equiy, and reurns for he prior monh are consisenly significan. Also, he coefficiens on size, book-o-marke equiy, and all hree lagged reurn measures are similar o hose repored in Table 4 for he period 1996 hrough June 2005. The coefficien on bea is posiive and, when idiosyncraic volailiy is included, he relaion wih reurns ges sronger. The findings sugges ha high implied idiosyncraic volailiy in monh should resul in high reurns in monh +1. Inuiively, he resuls are pleasing since here is a posiive heoreical relaion beween volailiy and reurns and because he idiosyncraic porion of implied volailiy makes up he majoriy of oal implied volailiy. Addiionally, implied volailiy, by definiion, is a forward looking measure, while realized volailiy is an ex-pos measure. Thus, he fac ha realized volailiy is insignifican is no surprising. The coefficien signs for he shor-sale consrain and he log of opion open ineres are also in he correc direcion. 15 The coefficien for he shor-sales consrain is significanly negaive a he 1% level, implying ha he higher he consrain, he lower he nex period s reurn. This suggess ha socks ha are overvalued due o difficuly in shoring he sock should have lower fuure reurns. Opion open ineres is a proxy for liquidiy, and he more liquid or acive he opion markes are, he less likely he sock suffers from shor-sale consrains. Open ineres always has a posiive coefficien ha is significan a he l% level, suggesing ha firms 14 We also examined resuls excluding socks below $5 wih lile change in resuls. 15 We also esimaed equaion (12) wih opion rading volume insead of open ineres. Volume and open ineres are highly correlaed and he resuls did no change. 18
wih more acive opions suffer less from shor-sale consrains. However, his variable is highly correlaed wih size. When λ = 2 0, he coefficien on open ineres is insignificanly negaive. My resuls so far for idiosyncraic risk are in conras o hose of Ang e al. (2006) and in agreemen wih economic heories which posi ha higher idiosyncraic volailiy socks should earn higher expeced reurns. My findings in Table 3 show ha implied idiosyncraic volailiy is an efficien bu upwardly biased predicor of fuure realized volailiy. My resuls in Table 5 show ha higher implied idiosyncraic volailiy resuls in higher fuure reurns. This suggess ha here is a premium for bearing implied idiosyncraic volailiy, a marke price of idiosyncraic volailiy risk ha may conribue o higher fuure reurns. Addiionally, i appears ha socks suffering from high shor-sale consrains or low liquidiy underperform socks wih limied shor-sale consrains or high liquidiy. Analysis Based on Single Sors Porfolio Reurn Analysis If here is a premium for bearing idiosyncraic volailiy risk, radiional asse pricing models will no capure his premium, and he resuls will appear o be low (high) abnormal reurns for low (high) idiosyncraic risk socks. Since my prior resuls show ha implied idiosyncraic volailiy forecass fuure idiosyncraic volailiy and reurns beer han hose forecass from saisical models, I furher analyze he former. I now examine, in a porfolio conex, reurns as a funcion of idiosyncraic risk. I consider he equal and value-weighed reurns o porfolios formed by soring individual securiies on he basis of implied idiosyncraic volailiy, realized idiosyncraic volailiy, he ORW_Raio, and he log of opion open ineres. My goal is o see wheher reurns are more closely associaed wih implied or realized idiosyncraic volailiy and if shor-sale consrains affec his relaion. To form he porfolios, my socks wih raded opions are independenly sored a he end of each monh ino five implied idiosyncraic volailiy, five realized idiosyncraic volailiy, five ORW_Raio, and five log of opion open ineres quiniles. I hen examine subsequen one-monh reurns. Mean values of various firm characerisics are presened for each of he porfolios in Table 6. Size and pas monhly reurns are inversely relaed o he wo idiosyncraic volailiy measures, while implied volailiy and ORW_Raio end o be posiively relaed o he wo 19
volailiy measures. Size and bea end o be posiively relaed o opion open ineres, while book-o-marke equiy and he ORW_Raio end o be negaively relaed o open ineres. Generally, relaions in Table 6 are as expeced. For each of he four sored parameers, I compue he ime-series mean and sandard deviaion of he monhly reurns over he enire sample period from January 1996 o June 2005. Addiionally, I form high minus low, zero-cos porfolios using he op and boom quiniles of he respecive sors. The four porfolios are formed as: (1) long high implied idiosyncraic volailiy and shor low implied idiosyncraic volailiy socks, (2) long high realized idiosyncraic volailiy and shor low realized idiosyncraic volailiy socks, (3) long high ORW_Raio and shor low ORW_Raio socks, and (4) long high opion open ineres and shor low opion open ineres socks. Abnormal reurns are alphas ha are esimaed for all porfolios by regressing equal and value-weighed monhly reurns on he four-facor model including he Fama and French (1993) marke, size, and value facors, and he Carhar (1997) momenum facor. The regression equaion is: where r p, α p + ψ 1, pmkt + ψ 2, psmb + ψ 3, phml + ψ 4, pumd + ε p, r 16 p is he reurn o a given porfolio. = (13) Table 7 repors he equal and value-weighed mean monhly raw reurns, sandard deviaion of reurns, and four-facor alphas wih -saisics in parenheses. Across he idiosyncraic volailiy porfolios he highes raw reurns and sandard deviaions are for he op quinile porfolios. The reurns decrease somewha monoonically for he equal-weighed porfolios. For he value-weighed porfolios, his paern holds rue for he sor on implied idiosyncraic volailiy, while here is no discernable paern for he realized idiosyncraic volailiy. For he ORW_Raio porfolios, he highes raw reurns are for he lowes quinile, for boh he equal and value-weighed porfolios. For he log of opion open ineres porfolios, higher reurns end o be associaed wih lower porfolios. For he idiosyncraic implied volailiy quiniles here are significanly posiive alphas a he 1% level in four of he five porfolios for boh equal and value weighing. For realized idiosyncraic volailiy quiniles, all five equal-weighed porfolios have significanly posiive 16 We repea all he analyses excluding socks whose prices are less han or equal o five dollars on he porfolio formaion dae. We do his ou of concern ha low-priced socks may disor he resuls for he broad sample of socks. The resuls are similar o hose presened. Addiionally, CAPM alphas and Fama and French (1993) hreefacor alphas were calculaed. The resuls are similar o he four-facor alphas we repor. 20
alphas, a he 1% level, while hree of five value-weighed porfolios have significanly posiive alphas a he 5% level or higher. The resuls of high-minus-low porfolios show ha he alphas for idiosyncraic volailiy are more posiive and significan han hose of realized volailiy. For he equal-weighed zero-cos porfolios, he coefficien is wice as big for implied volailiy hen for realized volailiy and he -saisic is significan a he 1% level versus he 5% level. For he value-weighed zero-cos porfolio he coefficien is posiive (bu insignifican) for implied volailiy and insignificanly negaive for realized volailiy. This provides preliminary evidence suggesing here is informaion in he idiosyncraic componen of implied volailiy beyond ha of realized volailiy. The general porfolio findings for idiosyncraic volailiy are conrary o he Ang e al. (2006) findings, bu consisen wih my Fama-MacBeh cross-secional analysis for individual securiies. One plausible explanaion is ha here is somehing unique abou socks wih opions on hem, alhough i is no clear why having an opion on a sock should aler he relaion beween reurns and idiosyncraic volailiy. A quesion arises as o how o inerpre hese significan alphas. I have been calling hem abnormal reurns because hey are unexplained by he four-facor model. However, here may be an omied variable in he model. As given, he four-facor model is srucured o price sysemaic risk, no o explain reurns on porfolios sored on idiosyncraic risk. Thus, an alernaive explanaion is ha idiosyncraic risk should be a priced facor in asse pricing models. In his case, he reurns would no be abnormal. For he ORW_Raio quiniles, low consrained porfolios ouperform high consrained porfolios for boh equal- and value weighed porfolios. High-minus-low porfolios have negaive and significan alphas a he 1% level. This is consisen wih earlier resuls, implying high shor-sale consrained porfolios are overvalued. There is lile variaion in he alphas across opion open ineres quiniles, refuing he noion ha more acive opions are less consrained han hose ha are less acive. Figure 1 shows he cumulaive dollar values o invesing in each of he following valueweighed sraegies. The firs is buying and holding he S&P 500. The dollar values of he S&P 500 are calculaed by iniially invesing $10,000 in 1996 and holding hrough June 2005. The second sraegy is going long high implied idiosyncraic volailiy and shor low implied idiosyncraic volailiy socks. The hird is going long high realized idiosyncraic volailiy and shor low realized idiosyncraic volailiy socks. The idiosyncraic risk porfolios have $5000 21
invesed long in he high volailiy socks and $5000 invesed shor in he low volailiy socks. As seen in he figure, reurns based on implied idiosyncraic volailiy are he bes, followed by he S&P 500, and hen realized idiosyncraic volailiy. $10,000 invesed in he implied idiosyncraic volailiy porfolio a he beginning of 1996 increases in value o abou $25,000 a he end of June, 2005. This is almos hree imes he cumulaive reurn of he equivalen S&P 500. The realized idiosyncraic volailiy porfolio has a negaive reurn for he period. Analysis Based on Double Sors The resuls I repor in Table 7 sugges ha boh implied and pas realized idiosyncraic volailiy can predic fuure sock reurns. However, i is no clear if hese represen wo separaely useful explanaory variables or if one risk measure subsumes he oher. In crosssecional regressions wih individual securiies I found ha implied idiosyncraic volailiy prediced fuure reurns, bu realized idiosyncraic volailiy does no. I now invesigae, in he conex of a porfolio analysis similar o Ang e al. (2006), if implied idiosyncraic volailiy is a beer predicor of fuure reurns han pas realized idiosyncraic volailiy. I es his relaion using a double-sor procedure. A he end of every monh I sor socks ino five porfolios, wih equal numbers of securiies in each, based on heir realized idiosyncraic volailiy over he prior 30 days. I hen form 25 porfolios, wih equal numbers of securiies, by soring he socks in each of hese five porfolios ino five sub-porfolios based on he implied idiosyncraic volailiy measured a he end of monh. 17 For each of he five iniial realized idiosyncraic volailiy sored porfolios, I form boh equal and value -weighed zerocos porfolios ha are long he high quinile of implied idiosyncraic volailiy socks and shor he low quinile of implied idiosyncraic volailiy socks. I measure reurns for he nex monh for each of hese en porfolios. Finally, I regress he reurns of hese en zero-cos porfolios on he four-facor model and focus on he alphas (abnormal reurns). I repor he alphas and heir -saisics in he firs row of Panel A in Table 8. For he equal-weighed porfolios he alphas are posiive and significan, a he 1% level, for all highminus-low implied idiosyncraic volailiy porfolios across realized idiosyncraic volailiy 17 The double soring procedure resuls in approximaely 50 socks wihin each of he 25 porfolios. 22
quiniles. For equal-weighed porfolios, no maer he level of realized idiosyncraic volailiy, higher implied idiosyncraic volailiy leads o higher fuure reurns. For he value-weighed porfolios, hree ou of five high-minus-low porfolio alphas are significan a he 5% level. These hree significan alphas are for porfolios wih higher realized idiosyncraic volailiy. I hen reverse he soring process, soring firs on implied idiosyncraic volailiy and hen on realized idiosyncraic volailiy, yielding 25 new porfolios. I form zero-cos porfolios for each of he five implied idiosyncraic volailiy porfolios as long he high quinile of realized idiosyncraic volailiy socks and shor he low quinile of realized idiosyncraic volailiy socks. I regress he reurns of hese zero-cos porfolios on he four-facor model and repor he alphas and -saisics in he second row of Panel A in Table 8. All bu one of he alphas is insignifican a he 5% level, he one significan alpha has a negaive sign, and seven of he en porfolios have negaive signs. This indicaes ha realized idiosyncraic volailiy does no significanly impac fuure reurns once implied idiosyncraic risk is conrolled for. Thus, resuls indicae ha implied idiosyncraic volailiy is imporan for predicing fuure reurns, bu realized idiosyncraic volailiy is uninformaive. Since implied idiosyncraic volailiy is posiively relaed o fuure sock reurns, I nex invesigae if his effec is pervasive across he firm characerisics of marke value of equiy (SIZE), book-o-marke equiy (B/M), shor-sale consrains (ORW_Raio), and liquidiy (OI). Each monh socks are independenly sored by SIZE, B/M, ORW_Raio, and OI, making five porfolios for each conaining equal numbers of socks. I sor he securiies in each of hese porfolios by implied idiosyncraic volailiy and form five sub-porfolios for each. I again place equal numbers of socks in each porfolio. Equal and value-weighed porfolios are formed for each of he 25 porfolios for he four double sors and he reurns are measured for he monh following he porfolio formaion dae. For each of he en SIZE, B/M, ORW_Raio, and OI caegories, zero-cos porfolios are formed ha are long he high quinile of implied idiosyncraic volailiy socks and shor he low quinile of implied idiosyncraic socks. There are 20 equal and 20 value-weighed zero-cos porfolios. I regress he reurns for each of hese zero-cos porfolios on he four-facor model. I repor he alphas and heir -saisics from hese regressions in Table 8, Panel B. For he sor on SIZE here are posiive and significan alphas a he 5% level or beer for he wo small SIZE quiniles for boh equal and value-weighed porfolios. All oher porfolios have 23
insignifican alphas excep for he larges size value-weighed quinile. For he sor on B/M here are posiive and significan alphas, a he 5% level or beer, for he hree highes B/M quiniles for boh equal and value-weighed porfolios. All oher porfolios have insignifican alphas. Thus, small size and high B/M firms ha have high implied idiosyncraic volailiy ouperform small size and high B/M firms wih low implied idiosyncraic volailiy. These findings sugges ha he well-documened size and book-o-marke equiy effecs may be linked o a posiive relaion beween reurns and implied idiosyncraic risk. Figure 2 shows he cumulaive dollar values o he S&P 500, he small SIZE quinile high minus low implied idiosyncraic volailiy porfolio, and he high B/M quinile high minus low implied idiosyncraic volailiy porfolio. I assume a $10,000 invesmen in each sraegy, saring in 1996. The figure is consisen wih he resuls in Table 8, Panel B, and show he srong, consisen performance of he high B/M and small size firms relaive o he marke. I is very ineresing o observe over he 2000 hrough 2003 period ha boh zero-cos porfolios have an average annual reurn above 30%, while he average annual marke reurn is -13%. The alphas across he ORW_Raio and OI show no discernable paern. For he en ORW_Raio porfolios, eigh of he alphas are significanly posiive a he 5% level or beer, and only one of he alphas has a negaive sign. For he OI porfolios, eigh ou of he en have posiive and significan alphas a he 5% level or beer. So while boh ORW_Raio and OI are relaed o firm reurns, hey do no seem o be srongly relaed o he endency of high implied idiosyncraic volailiy socks o ouperform low implied idiosyncraic volailiy socks. 24
TABLE 1: Descripive Saisics of Opion Firm Sample This able repors he mean, median, 5 h percenile, and 95 h percenile values for firm characerisics wihin he opion firm sample from January 1996 hrough June 2005. All available monhly daa for each firm is used. SIZE is price imes shares ousanding, B/M is book-o-marke equiy, β is calculaed from he marke model using he pas 60 monhs of reurns, ORW_Raio is he Ofek, Richardson, and Whielaw (2004) shor-sales consrain raio, and OI is he log of opion open ineres. The six volailiy measures are: 1) σ IV, he average firm implied volailiy, 2) σ RV, he average firm realized volailiy, calculaed as he annualized sandard deviaion of he curren monh s daily reurns, 3) σ IV _ idio, he idiosyncraic porion of implied volailiy coming from equaion (2), 4) σ RV _ idio, he idiosyncraic porion of realized volailiy calculaed using he marke model, 5), he idiosyncraic porion of σ EG _ idio volailiy coming from he EGARCH model in equaion (5), and 6) σ AR _ idio, he idiosyncraic porion of volailiy coming from he AR(2) model in equaion (6). Obs by firm is he average number of observaions for any given firm in he sample. Firms by monh is he average number of firms for any given monh in he sample. mean median 5h 95h SIZE ($ housands) 6,165 1,283 179 23,633 B/M 0.52 0.45 0.06 1.04 Bea 1.20 1.03 0.27 2.66 ORW_Raio 0.08 0.06-1.05 1.21 OI 11.22 11.09 8.25 14.71 σ IV 50.7% 46.6% 27.5% 85.6% σ RV 48.1% 43.2% 24.4% 85.5% σ IV _ idio 35.3% 32.9% 15.4% 64.8% σ RV _ idio 38.3% 35.1% 19.7% 67.4% σ EG _ idio 39.0% 34.1% 13.9% 79.1% σ AR _ idio 43.1% 37.9% 16.7% 85.9% Obs by Firm 75 79 17 114 Firms by Monh 1,704 1,643 1,421 2,018 25
TABLE 2: Forecasing Fuure Realized Volailiy This able shows he esimaion resuls of he following models: σ σ RV _ M, + 1 = α + ξ1σ IV _ M, + ξ 2σ RV _ M, + ε + 1 RV, + 1 = α j + ξ1, jσ IV, + ξ 2, jσ RV, + ε + 1 where σ RV is realized volailiy, calculaed as he annualized sandard deviaion of monh daily reurns, σ IV is he implied volailiy for monh, ε is he residual, and α andξ represen coefficiens o be esimaed. The firs model is for he marke and he second is for individual firms. Panel A presens he marke coefficiens, wih -saisics in parenheses, where realized volailiy is for he S&P 500 index and implied volailiy is he VIX index. Panel B presens he firm-level coefficiens, wih implied volailiies from OpionMerics. For he firm-level resuls, I repor he mean and median coefficien esimaes for he 1310 firms ha have a leas 60 observaions. The numbers in brackes are he 25 h and 75 h percenile values of he coefficiens. In he firs column ξ 2 is resriced o zero. In parenheses are -saisics from reverse Fama and Macbeh (1973) regressions, where he model is esimaed for each firm hrough ime and hen -saisics are from he cross-secional disribuion of coefficiens across firms. The sample period is from 1996 hrough June 2005. * is significan a he 5% level. ** is significan a he 1% level. ξ 1 ξ 2 Panel A: Marke Esimaes Panel B: Firm-Level Esimaes Mean/Median Mean/Median ξ 2 = 0 ξ 2 = 0 0.728 0.599 0.731 / 0.738 0.611 /0.603 (10.15)** (5.43)** [0.540 / 0.918] [0.408 / 0.809] (51.94)** (77.62)** 0.160 0.136/0.124 (1.52) [0.021 / 0.560] (27.66)** -0.003-0.001 0.099 / 0.087 0.092 / 0.080 (0.21) (0.02) [0.029 / 0.154] [0.029 / 0.137] (18.63)** (33.35)** 26
TABLE 3: Forecasing Firm Fuure Realized Volailiy wih Idiosyncraic Volailiy This able shows he esimaion resuls of he following model on individual socks: σ RV _ idio, + 1 = α j + ψ 1, jσ IV _ idio, + ψ 2, jσ EG _ idio, + ψ 3, jσ AR _ idio, + ψ 4, jσ RV _ idio, + ε + 1 The four volailiy measures are: 1) σ, he idiosyncraic porion of implied volailiy coming from equaion (2), IV _ idio 2) σ EG _ idio, he idiosyncraic porion of volailiy coming from he EGARCH model in equaion (5), 3) σ AR _ idio idiosyncraic porion of volailiy coming from he AR(2) model in equaion (6), and 4) σ RV _ idio, he, he idiosyncraic porion of realized volailiy calculaed using he marke model. ε is he residual, and α and ψ represen coefficiens o be esimaed. I repor he mean and median coefficien esimaes for he 1255 firms ha have a leas 60 observaions. The numbers in brackes are he 25 h and 75 h percenile values of he coefficiens. In parenheses are -saisics from reverse Fama and MacBeh (1973) regressions, where he model is esimaed for each firm hrough ime and hen -saisics are from he cross-secional disribuion of coefficiens across firms. The sample period is from 1996 hrough June 2005. * is significan a he 5% level. ** is significan a he 1% level. ψ 1 Mean/Median Mean/Median Mean/Median Mean/Median 0.365 / 0.354 0.330 / 0.312 [0.197 / 0.519] [0.149 / 0.485] (2.84)** (2.43)* ψ 2 0.182 / 0.185-0.006 / 0.001 [0.019 / 0.337] [-0.194 / 0.188] (1.39) (0.87) ψ 3 0.296 / 0.277 0.174 / 0.157 [0.093 / 0.492] [-0.106 / 0.419] (1.74) (1.04) ψ 4 α 0.184 / 0.185 0.323 / 0.326 0.295 / 0.298 0.157 / 0.156 [0.067 / 0.305] [0.199 / 0.448] [0.171 / 0.420] [0.044 / 0.269] (1.95) (3.48)** (3.18)** (1.73) 0.169 / 0.150 0.186 / 0.150 0.148 / 0.115 0.133 / 0.104 [0.106 / 0.210] [0.098 / 0.239] [0.055 / 0.206] [0.049 / 0.184] (3.76)** (2.69)** (1.96)* (1.74) 27
TABLE 4: Fama-MacBeh Esimaion wih All Available Socks This able shows summary resuls of he Fama-MacBeh monhly cross-secional regressions wih fuure one-monh reurns he dependen variable, = α + + + + r + 1 λ1σ RV _ idio, λ2 LSIZE λ3lbm λ4r + λ 5 r 11: 1 + λ6r 35: 12 + λ7β + ε + 1 σ RV _ idio is he idiosyncraic porion of realized volailiy calculaed from equaion (3). LSIZE is he log of marke equiy and LBM is he log of he raio of book-o-marke equiy. The hree reurns ha are independen variables precede he dependen variable reurn by one monh, he eleven monhs prior o he firs reurn independen variable, and he 24 monhs prior o he second independen reurn variable, respecively. β is calculaed from he marke model using he pas 60 monhs of reurns. α and λ s are he coefficiens o be esimaed. The cross-secional regressions are esimaed over wo separae ime periods. The firs is he same ime period used in Ang e al. (2006), 1963-2000. The second ime period is from 1996 hrough June 2005 and corresponds o he period of my opions daa. The ime-series average of he coefficien esimaes are repored wih he associaed -saisics in parenheses. * is significan a he 5% level. ** is significan a he 1% level. σ RV _ idio 1963-2000 1996 - June 2005-0.0576-0.0492 0.0182-0.0575 (1.19) (1.42) (0.19) (1.05) LSIZE -0.0009-0.0016 (2.15)* (1.69) LBM 0.0031 0.0034 (4.14)** (2.21)* r -0.0725-0.0504 (19.01)** (5.54)** r -11:-1 0.0072 0.0023 (4.15)** (0.63) r -35:-12-0.0035-0.0051 (4.36)** (2.52)* β -0.0054 0.0021 (0.76) (0.84) 28
TABLE 5: Fama-MacBeh Esimaion on Socks wih Opions This able shows summary resuls of he Fama-MacBeh monhly cross-secional regressions wih fuure one-monh reurns as he dependen variable, r = α + λ σ + λ LSIZE + λ LBM + λ r + λ r + λ r + 1 1 + λ β 7 RV _ idio, + λ σ 8 2 IV _ idio, + λ σ 9 EG _ idio, AR _ idio, _ 12 + 1 σ RV _ idio is he idiosyncraic porion of realized volailiy from equaion (3). LSIZE is he log of marke equiy and LBM is he log of book-o-marke equiy. The hree reurns ha are independen variables precede he dependen variable by one monh, he eleven monhs prior o he firs reurn independen variable, and he 24 monhs prior o he second independen reurn variable, respecively. β is calculaed from he marke model using he pas 60 monhs of reurns, σ IV _ idio is he idiosyncraic porion of implied volailiy from equaion, σ EG _ idio is he idiosyncraic porion of volailiy from he EGARCH model in equaion (5), σ AR _ idio is he idiosyncraic porion of volailiy from he AR(2) model in equaion (6), ORW_Raio is he Ofek, Richardson, and Whielaw (2004) shor sales consrain raio, and OI is he log of monhly firm opion open ineres plus one. The ime-series average of he coefficien esimaes are repored wih -saisics in parenheses. (1) (2) (3) (4) (5) (6) (7) (8) (9) (10) σ RV _ idio 0.0116-0.0021 0.0100 0.0092-0.0026-0.0036 0.0007 (1.30) (0.43) (0.69) (1.58) (0.55) (0.75) (0.14) LSIZE -0.0048-0.0040-0.0035-0.0019-0.0018-0.0032-0.0030-0.0018-0.0050 (4.54)** (4.39)** (4.20)** (2.31)* (2.18)* ( 3.88)** ( 3.59)** (2.23)* (5.09)** LBM 0.0053 0.0058 0.0059 0.0065 0.0064 0.0049 0.0049 0.0051 0.0049 0.0063 (4.11)** (4.00)** (4.52)** ( 5.00)** ( 5.05)** (4.92)** (5.07)** (5.43)** (5.17)** ( 6.29)** r -0.0240-0.0244-0.0224-0.0216-0.0216-0.0214-0.0221-0.0208-0.0193-0.0185 (2.14)* (2.46)* (2.47)* (2.38)* (2.41)* ( 2.54)** ( 2.61)** ( 2.56)** (2.38)* (2.28)* r -11:-1 0.0027 0.0023 0.0022 0.0023 0.0022 0.0009 0.0007 0.0010 0.0019 0.0017 (1.18) (1.11) (1.09) (1.14) (1.13) (0.47) (0.37) (0.52) (0.96) (0.89) r -35:-12-0.0014-0.0005-0.0005-0.0006-0.0006-0.0008-0.0008-0.0008-0.0006-0.0004 (1.77) (0.83) (0.89) (1.02) (1.01) (1.44) (1.54) (1.45) (1.20) (0.82) β 0.0017 0.0031 0.0051 0.0061 0.0025 0.0020 0.0063 0.0040 0.0058 (0.53) (0.95) (1.42) (1.77) (0.80) (0.65) (1.81) (1.16) (1.75) σ IV _ idio 0.0350 0.0371 0.0352 0.0307 0.0426 ( 4.20)** ( 5.67)** (5.56)** ( 4.92)** ( 5.77)** σ EG _ idio 0.0124 0.0031 (2.20)* (0.45) σ AR _ idio 0.0148 0.0034 (2.42)* (0.46) ORW_Raio -0.0027-0.0027 (4.43)** (4.33)** OI 0.0026-0.0001 (4.17)** (0.18) α 0.1276 0. 1113 0. 1072 0. 0777 0.0745 0.093 0. 0904 0.0651 0.0854 0.0565 ( 8.22)** ( 8.07)** ( 7.17)** ( 4.45)** ( 4.41)** (6. 21)** (5.79)** (3.85)** ( 5.28)** ( 4.82)** 3 + λ σ 10 4 5 11: 1 + λ ORW 11 6 35: 12 Raio + λ OI + ε 29
TABLE 6: Mean Values of Firm Characerisics for Sored Porfolios This able repors mean values of characerisics of porfolios whose securiies are sored ino quiniles four differen ways. Securiies are sored by σ, he idiosyncraic porion of implied volailiy from equaion IV _ idio (2), σ RV _ idio, he idiosyncraic porion of realized volailiy from equaion (3), ORW_Raio, he Ofek, Richardson, and Whielaw (2004) shor sales consrain raio, and OI, he log of monhly firm opion open ineres plus one. Size is price imes shares ousanding, B/M is book-o-marke equiy, implied volailiies are from OpionMerics, bea is calculaed from he marke model using he pas 60 monhs of reurns, OI is he log of opion open ineres, and he pas one monh reurn is from he prior monh. 1(Low) 2 3 4 5(High) σ IV _ idio Size 13,900 11,500 5,990 3,068 1,302 B/M 0.40 0.40 0.42 0.45 0.50 Implied Volailiy 36.4% 33.3% 40.7% 51.4% 73.0% Bea 1.55 0.89 0.94 1.07 1.27 ORW_Raio 0.03 0.01 0.02 0.08 0.15 OI 11.79 11.39 11.18 11.11 11.15 Pas Monh Reurn 2.1% 1.9% 2.0% 1.8% 1.4% σ RV _ idio Size 10,890 10,700 7,665 4,509 2,264 B/M 0.42 0.41 0.43 0.45 0.44 Implied Volailiy 36.4% 36.4% 42.9% 52.3% 66.9% Bea 1.18 0.87 1.00 1.20 1.50 ORW_Raio 0.03 0.02 0.06 0.09 0.09 OI 11.25 11.30 11.32 11.32 11.44 Pas Monh Reurn 2.0% 1.8% 1.8% 1.9% 1.5% ORW_Raio Size 5,392 7,245 8,613 5,860 3,712 B/M 0.49 0.41 0.39 0.42 0.49 Implied Volailiy 52.6% 48.6% 47.0% 49.4% 56.0% Bea 1.11 1.14 1.11 1.15 1.24 ORW_Raio -0.99-0.17 0.07 0.31 1.18 OI 10.97 11.34 11.49 11.30 10.98 Pas Monh Reurn 1.1% 2.0% 2.5% 2.2% 1.6% OI Size 1,040 1,503 2,211 3,698 22,400 B/M 0.55 0.51 0.45 0.41 0.33 Implied Volailiy 47.1% 50.2% 52.6% 53.7% 49.9% Bea 0.94 1.08 1.16 1.24 1.31 ORW_Raio 0.10 0.10 0.09 0.07 0.04 OI 8.70 10.23 11.12 12.10 13.94 Pas Monh Reurn 1.7% 1.9% 2.1% 1.9% 1.8% 30
TABLE 7: Idiosyncraic Porfolio Percenage Reurns This able shows he raw and abnormal percenage monhly reurns o porfolios formed by soring socks based on implied idiosyncraic volailiy ( σ realized idiosyncraic volailiy ( σ RV _ idio ) as defined by equaions (2) and (3), respecively. A he end of each monh, firms are sored ino one of five idiosyncraic volailiy porfolios. Porfolio 1 (5) conains low (high) idiosyncraic volailiy firms. Porfolio reurns are calculaed over he following monh +1. This is done separaely for boh implied and realized idiosyncraic volailiy. The raw monhly reurn mean and sandard deviaion (sd) are given for boh equal and value-weighed porfolios. The alpha is from he four-facor Fama-French and Cahar model, and is repored for boh he equal and value-weighed porfolio. The high-low alpha is from a regression of he reurns o porfolio 5 minus hose of porfolio 1. A similar analysis is conduced for porfolios formed by soring securiies on he basis of ORW_Raio, which is he Ofek, Richardson, and Whielaw (2004) shor sales consrain raio, and he log of opion open ineres plus one, OI. The -saisics are given in parenheses. * is significan a he 5% level. ** is significan a he 1% level. IV _ idio ) and Equal Weighed Value Weighed 1(Low) 2 3 4 5(High) High-Low 1(Low) 2 3 4 5(High) High-Low σ IV _ idio mean 1.47 0.92 1.38 1.86 3.09 1.05 0.74 1.08 1.40 1.46 sd 5.29 4.04 4.67 5.86 8.23 5.27 3.67 5.24 6.67 9.50 alpha 0.653 0.271 0.660 1.169 2.566 1.913 0.334 0.363 0.708 1.060 0.976 0.642 -sa (2.83)** (1.91) (4.16)** (5.94)** (9.10)** (5.29)** (1.69) (2.83)** (3.29)** (4.05)** (2.93)** (1.50) σ RV _ idio mean 1.61 1.33 1.62 1.81 2.37 1.00 0.87 1.04 0.98 0.87 sd 4.44 4.31 4.71 6.09 8.49 4.23 4.19 4.83 6.35 8.92 alpha 0.996 0.549 0.913 1.088 1.824 0.828 0.483 0.284 0.724 0.528 0.435-0.048 -sa (4.71)** (3.75)** (5.31)** (5.53)** (6.49)** (2.36)* (2.57)* (1.91) (3.94)** (2.06)* (1.26) (0.11) ORW_Raio mean 2.91 1.74 1.36 1.40 1.85 1.15 1.00 0.97 0.94 0.27 sd 5.78 5.71 5.51 5.83 5.77 4.38 5.22 5.27 4.77 4.42 alpha 2.324 0.986 0.675 0.681 1.218-1.106 0.897 0.517 0.449 0.336-0.288-1.185 -sa (10.82)** (6.88)** (4.97)** (4.85)** (5.83)** (6.40)** (5.10)** (3.87)** (3.60)** (2.67)** (1.52) (4.70)** OI mean 1.97 2.13 1.95 1.66 1.55 1.15 1.14 1.10 0.99 0.88 sd 4.79 5.31 5.75 6.24 6.74 3.98 4.13 4.29 4.30 5.01 alpha 1.172 1.382 1.216 1.049 1.063-0.109 0.341 0.299 0.294 0.277 0.496 0.155 -sa (6.69)** (8.47)** (6.70)** (6.52)** (6.48)** (0.50) (2.16)* (2.11)* (2.13)* (2.28)* (7.89)** (0.81) 31
TABLE 8: Double-Sored High Minus Low Percenage Porfolio Reurns This able shows he abnormal percenage monhly reurns from he four-facor Fama-French and Carhar model on high minus low double-sored equal and value- weighed porfolios. A he end of each monh firms are sored ino one of five porfolios, and hen each porfolio is sored ino five addiional porfolios for a oal of 25 porfolios. Each porfolio s reurns are calculaed over he following monh. Panel A shows wo double-sors. The firs is a sor of realized idiosyncraic volailiy ( σ RV _ idio ) and hen implied idiosyncraic volailiy ( σ IV _ idio ). The second sors implied idiosyncraic volailiy ( σ IV _ idio ) and hen realized idiosyncraic volailiy ( σ RV _ idio ). In Panel B, firms are sored by characerisic, and hen by idiosyncraic implied volailiy ( σ IV _ idio ). SIZE is calculaed as he price imes shares ousanding, B/M is book value of equiy divided by marke equiy, ORW_Raio is he Ofek, Richardson, and Whielaw (2004) shor sales consrain raio, and OI is he log of opion open ineres plus one. The -saisics are given in parenheses. * is significan a he 5% level. ** is significan a he 1% level. Equal Weighed Value Weighed Panel A 1(Low) 2 3 4 5(High) 1(Low) 2 3 4 5(High) σ RV _ idio ( IV _ idio σ ) 3.288 0.973 1.200 1.684 2.207 1.277 0.819 1.159 1.053 1.645 (4.90)** (3.16)** (4.21)** (5.67)** (5.11)** (1.52) (1.81) (2.04)* (2.14)* (2.51)* σ IV _ idio ( RV _ idio σ ) -0.234-0.408-0.750-0.331 0.402 0.164-0.450-0.966-0.403 0.000 (0.64) (1.51) (2.58)* (0.92) (0.68) (0.29) (1.00) (1.54) (0.59) (0.00) Pan elb SIZE( σ IV _ idio ) 3.270 1.112 0.546 0.781 0.293 2.532 1.109 0.508 0.807 0.888 (5.84)** (2.16)* (1.26) (1.78) (0.78) (4.57)** (2.17)* (1.20) (1.83) (2.23)* B/M( σ IV _ idio ) 0.767 0.744 2.254 2.288 3.919-0.836 0.325 1.722 1.831 3.126 (1.38) (1.33) (4.52)** (4.36)** (8.14)** (1.04) (0.42) (2.46)* (2.88)** (4.53)** ORW_Raio( σ IV _ idio ) 2.700 1.152 1.022 2.207 2.233 2.270-0.152 0.313 1.923 1.283 (5.41)** (2.55)* (2.32)* (4.50)** (4.88)** (3.48)** (0.23) (0.47) (3.32)** (2.30)* OI( σ IV _ idio ) 2.004 2.543 2.334 1.489 1.222 1.259 1.269 1.456 0.302 0.922 (5.80)** (5.81)** (5.10)** (2.86)** (2.27)* (3.67)** (3.01)** (2.98)** (0.59) (1.76) 32
$25,000 S&P 500 Implied Idiosyncraic Volailiy Realized Idiosyncraic Volailiy $20,000 $15,000 $10,000 $5,000 $- 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 Figure 1: Cumulaive Dollar Values for Implied and Realized Idiosyncraic Volailiy This figure demonsraes he cumulaive dollar values o invesing in one of he following sraegies. Firs, buy and hold he S&P 500. Second go long high implied idiosyncraic volailiy and shor low implied idiosyncraic volailiy socks. Third, go long high realized idiosyncraic volailiy and shor low realized idiosyncraic volailiy socks. The las wo porfolios are value weighed and formed every monh by ranking he idiosyncraic volailiies a he end of he monh and hen holding hem for one monh. The dollar values are calculaed by iniially invesing $10,000 in each sraegy in 1996 and holding hrough June 2005. 33
$300,000 S&P 500 Small Size High B/M $250,000 $200,000 $150,000 $100,000 $50,000 $- 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 Figure 2: Small Size and High Book-o-Marke Equiy Cumulaive Dollar Values This figure demonsraes he cumulaive dollar values o invesing in one of he following sraegies. Firs, buy and hold he S&P 500. Second, go long high idiosyncraic implied volailiy and shor low idiosyncraic implied volailiy socks in he small size caegory. Third, go long high idiosyncraic implied volailiy and shor low idiosyncraic implied volailiy socks in he high B/M caegory. The porfolios are value-weighed, and formed every monh by ranking he implied volailiies a he end of he monh and hen holding hem for one monh. The dollar values are calculaed by iniially invesing $10,000 in each sraegy in 1996 and holding hrough June 2005. 34
CHAPTER 2 OPTION MARKET EFFICIENCY AND EARNINGS ANNOUNCEMENTS Daa Descripion Several sources are uilized o acquire he daa. Individual company daily implied reurn volailiy, opion volume and opion prices, from January 1996 hrough April 2006, are available from OpionMerics. 18 For each firm, implied volailiies are calculaed by OpionMerics using American or European models where appropriae. A sandardized implied volailiy is calculaed by employing he mos weigh on implied volailiies wih a-he-money opions. Opion prices are used for he formaion of zero-cos arbirage porfolios. The oal number of firm observaions for he (-30, 1) sample is 35,507 wih a oal of 3,957 unique firms. The oal number of firm observaions for he (-20, 1) sample is 31,814 wih a oal of 3,833 unique firms. The oal number of firm observaions for he (-10, 1) sample is 27,075 wih a oal of 3,707 unique firms. The oal number of firm observaions for he (-3, 1) sample is 19,507 wih a oal of 3,207 unique firms. I ake acual quarerly earnings per share (EPS), EPS announcemen daes, and quarerly consensus EPS forecass from he I/B/E/S daabase. The consensus forecas is he mean of analyss EPS forecass immediaely prior o he earnings announcemen and is conained in he I/B/E/S summary hisory file. 19 The summary hisory file consiss of a complee updae of I/B/E/S hisorical daa ha includes he laes monh s daa and hisorical daa adjused for corporae acions and correcions, such as sock splis. I obain sock reurns, share prices and number of shares ousanding from CRSP. 20 CRSP daa I obain is resriced o firms wih raded opions and o he period 1996-2006. For he opion sample we use all firms ha have opions raded on hem wih he condiion ha here 18 OpionMerics is a financial research and consuling firm specializing in economeric analysis of he opions markes. 19 The monhly consensus forecas conains analyss EPS forecass up o he Thursday before he hird Friday of every monh. For each quarer, I use he monhly consensus forecas from he monh closes o he earnings announcemen dae. For example, if he earnings announcemen comes before he hird Thursday of he monh, hen we use he monhly consensus forecas from he prior monh. 20 I exclude all ETFs, foreign socks, financial firms, and uiliies. I include only firms wih a 10 or 11 share code. The 35
is a leas 230 rading days of prior sock reurn daa. This is necessary for he calculaion of he firm s bea. To esimae firm j s bea, daily sock reurns, r, are regressed on marke reurns using a period of 31 o 230 rading days before he EPS announcemen. The model is: r = α + β MRET + ε q, jq, jq, q, jq,, (1) where MRET q, is he reurn on he CRSP value weighed-index for quarer q, on day, and is he reurn for firm in quarer q, on day. r jq,, Mehodology My hypohesis is ha informaion abou earnings announcemen surprises is imbedded in opion prices prior o he announcemen. I also hypohesize ha his informaion is refleced in opion prices before i is refleced in sock prices. To es his, I examine he implied volailiy skew and wheher he skew can predic EPS announcemen surprises. Specifically, I sor socks ino quiniles based on BKM and implied volailiy difference beween OTM and ITM call opions (call IV difference), OTM and ITM pu opions (pu IV difference), and consider abnormal reurns o a buy and hold sraegy for sock and opions hrough he day afer he earnings announcemen. I expec o see greaer abnormal reurns o firms in he high skew quinile if he opions marke is correcly anicipaing SUEs. Nex, using he pu-call pariy relaion, I form zero-cos porfolios of opions and sock for firms sored ino quiniles based on volailiy skew and consider wheher abnormal reurns o his sraegy exis. The final par of my analysis compares individual sock reurns wih individual opion reurns. For he remainder of he analysis, I examine he volailiy skew a 30, 20, 10, and 3 rading days prior o he earnings announcemen. The objecive is o provide various windows o examine wheher informaion is in sock and/or opion prices. I use 30 days prior as a reasonable saring poin a which earnings informaion may begin o appear in opion prices. I hypohesize ha a 30 rading days prior o he earnings announcemen informaion is no ye in sock prices. However, we consider he ransiion periods of 20 and 10 days prior o he announcemen dae because earnings informaion may no be priced ino opions 30 days before he announcemen. 36
Similarly, a 3 days before, earnings informaion may already be priced ino boh sock and opions. Volailiy Skew If informaion abou earnings announcemen surprises is imbedded in opion prices prior o he announcemen, hen informaion should be refleced in OTM implied volailiies being high relaive o ITM implied volailiies. To capure informaion across he enire implied volailiy skew, I employ he non-parameric esimaion of risk-neural skewness calculaed in Bakshi, Kapadia, and Madan (2003) and used by Doran, Peerson, and Tarran (2007). The variable is defined as: BKM = e rτ W(, τ) 3μ(, τ) e rτ ν(, τ) + 3μ(, τ) 3 rτ 2 ( e ν(, τ) μ(, τ) )2 2 (2) where W (, τ ), μ(, τ), and ν(, τ) are defined in Appendix A. This measure expresses he enire volailiy skew as a single value, which provides a simple alernaive o dividing he skew ino pars. For example, BKM becomes more posiive when OTM implied volailiies for calls increase, and BKM becomes more negaive when OTM implied volailiies for pus increase. A disadvanage in using his ype of measure is ha i canno idenify from which par of he skew he informaion conen comes. I compue volailiy skew for each firm using BKM a 30, 20, 10, and 3 rading days prior o he earnings announcemen dae. I also employ an alernaive measure ha allows me o examine porions of he volailiy skew. Following Baes (2000) and Doran, Peerson, and Tarran (2007), I use he call volailiy skew o anicipae good news and he pu volailiy skew o anicipae bad news. 21 consruc he difference beween OTM and ITM implied volailiies as: φσ = σ σ φσ C C C jq,, o i P P P jq,, o i To do his I (3) = σ σ (4) 21 Doran, Peerson, and Tarran (2007) find ha he call skew changes more for good news, and ha he pu skew changes more for bad news. 37
where C σ o and C σ i represen, respecively, OTM and ITM implied volailiies for calls, P σ i represen, respecively, OTM and ITM implied volailiies for pus, and difference), and P φσ jq,, P σ o and (call IV (pu IV difference), represen he difference beween OTM and ITM implied volailiies for calls and pus, respecively for firm in quarer q, measured 30 rading days prior o he acual earnings announcemen. C φσ jq,,, I define moneyness as [ K / s e τ ], where K is he srike price, is he price of he jq,, r f q sock for firm in quarer q, a ime, which is 30 rading days prior o he acual earnings announcemen, s jq,, r f, q is he risk-free rae in quarer q and τ is he ime o mauriy of he opion. The moneyness caegories are similar o hose given in Bakshi and Kapadia (2003). ATM opions include he moneyness bin inerval from.975 o 1.025. OTM pus and ITM call opions are assigned o a moneyness bin inerval of.925 o.975. OTM calls and ITM pus have a moneyness bin inerval of 1.025 o 1.075. 22 For each sock here may be more han one opion ha falls wihin he range of each moneyness bin. Therefore, for each moneyness bin I selec only he opion ha mees he following crieria: for ATM opions I selec he opion ha rf qτ, minimizes he absolue value of [ K/ s e 1], for OTM pus and ITM calls I selec he jq,, opion ha minimizes he absolue value of [ K/ sjq e r f q,,,.95], and for OTM calls and ITM pus, I selec he opion ha minimizes he absolue value of K/ s e τ 1.05]. τ [ jq,, The measures given in equaions (3) and (4) represen levels of he volailiy skew. As he earnings announcemen dae approaches, I expec ha hese measures will be higher if earnings informaion is impounded ino OTM opions sooner relaive o ITM opions. I repea my analysis and re-compue my measures of he implied volailiy skew, P C BKM, φσ jq,, and φσ jq,,, a poins in ime equal o 20, 10, and 3 rading days prior o he jq,, EPS announcemen dae. r f q Sandardized Unexpeced Earnings 22 For example, he 1.025 o 1.075 moneyness inerval includes opions wih srike prices ha are approximaely beween 2.5% and 7.5% above he curren level of he sock price. 38
Sandardized unexpeced earnings (SUE) is defined as acual quarerly earnings per share from he IBES deail file minus expeced quarerly earnings, divided by he absolue value of he consensus forecass: SUE jq, E Eˆ jq, jq, = (5) abs( Eˆ ) jq, where SUE jq, is my sandardized unexpeced earnings measure for firm j in quarer q, E jq, is he acual quarerly earnings per share for firm j in quarer q, ( jq E ˆ jq, is he quarerly consensus EPS forecas, and abs E ˆ, ) is he absolue value of he quarerly consensus EPS forecas obained from he I/B/E/S daabase. I calculae SUEs for every quarer over he period January 1996 hrough April 2006. Observaions are required o have a leas hree forecass. Relaionship Beween SUE and he Volailiy Skew My hypohesis is ha informaion abou earnings announcemen surprises is imbedded in opion prices prior o he earnings announcemen. I also hypohesize ha his informaion is refleced in opion prices before i is refleced in sock prices. To es his, I examine he implied volailiy skew, and wheher a relaionship beween he skew and EPS announcemen surprises exiss. Tha is, I examine he percenage of earnings surprises which are posiive afer dividing he sample ino quiniles according o BKM, he implied volailiy difference beween OTM and ITM call opions, C φσ jq,, and ITM pu opions, P φσ jq,, (call IV difference), and he implied volailiy difference beween OTM (pu IV difference). I also examine he differences beween high and low quiniles for each measure. This analysis is done a 30, 20, 10, and 3 rading days before he acual earnings announcemen. Abnormal Sock Reurns Following implied volailiy sors, I examine abnormal sock reurns hrough he day afer earnings announcemens. Each quarer I sor socks ino quiniles based on BKM jq,,. If he 39
opions marke is correcly anicipaing SUEs and he informaion is no ye in sock prices, hen I expec o see greaer values of abnormal reurns o firms in he larges skew quiniles. I calculae daily abnormal sock reurns in each quinile as he difference beween he sock s acual reurn and expeced reurn, as esimaed by he marke model. Average abnormal reurns in each quinile are hen compued. The model is AR = r ( ˆ α + ˆ β MRET ) (6) jq,, jq,, jq, jq, q, AR jq,, where is he abnormal reurn for firm in quarer q, measured on day, which is 30 r jq,, rading days prior o he acual announcemen, is he reurn for firm in quarer q, on day, and ˆα and β, are esimaed coefficiens from he marke model specified in equaion (1). For jq, ˆ jq example, each quarer, a 30 rading days prior o he acual earnings announcemen, I sor socks ino quiniles based on BKM jq,, and iniiae long sock posiions. Daily abnormal reurns for each firm and average daily abnormal reurns across firms in each quinile are compued. All posiions iniiaed 30 rading days before he EPS announcemen are held unil one day afer he acual announcemen. I compue daily abnormal reurns o each posiion hrough one day afer he earnings announcemen in order o beer undersand when earnings informaion acually begins o appear in sock prices. I also perform a similar analysis by soring socks ino quiniles using my alernaive P C measure and. I expec o see greaer absolue values of abnormal reurns o firms φσ jq,, φσ jq,, in he larges skew quiniles. P The enire process is repeaed for each of my measures, BKM jq,,, jq,, and C φσ φσ jq,, based on soring 20, 10, and 3 rading days prior o he acual earnings announcemen. Abnormal Opion Reurns I consider This par of my analysis compares abnormal sock reurns wih abnormal opion reurns. BKM jq,, a 30 rading days prior o an earnings announcemen for each sock in my sample, and subsequenly sor socks ino quiniles based on BKM jq,,. Then I iniiae my sock 40
and opion posiions. Posiions are held from 30 rading days prior o earnings announcemen unil one day afer earnings announcemen. If he implied volailiy skew is higher, his means ha opion prices have already adjused in expecaion of an earnings surprise bu he sock has no, hen a sock posiion should subsequenly ouperform an equivalen posiion in opions. Daily abnormal reurns o opions are compued as he difference beween he opion s acual reurn and expeced reurn as esimaed using he opions bea and he CAPM. Average daily abnormal reurns for opions in each quinile are hen compued. I esimae he bea of a pu (call) opion using sock and opion daa from he period 31 o 230 rading days before announcemen. Following Coval and Shumway (2001), he opions bea is compued as 2 s jq,, ln( sjq,,/ K) + ( rf, q λjq, + σ jq,,/ 2) τ P ˆ s β jq, = N 1 β Pjq,, σ jq,, τ 2 s jq,, ln( sjq,,/ K) + ( rf, q λjq, + σ jq,,/ 2) τ C ˆ s β jq, = N β jq, C jq,, σ jq,, τ where N [ ] is he cumulaive normal disribuion, K is he srike price, τ is he ime o mauriy, σ is he implied volailiy, r f, q is he risk-free ineres rae in quarer q as proxied for by he 3- monh Treasury bill rae available from he Federal Reserve websie, and,, and j, q s jq,, P jq,, C jq,, (7) (8) are he sock price, pu price, and call price, respecively, for firm in quarer q, on day. ˆ s jq, β is he bea of he sock for firm j in quarer q, esimaed from equaion (1), and λ jq, is he dividend yield of firm j in quarer q, as proxied for by he annual dividend rae from Compusa. I compue opion beas from equaions (7) and (8) for each opion in my sample using he moneyness caegories and previous crieria. To compue daily abnormal opion reurns, I follow Doran (2007) and use a CAPM ype model and esimae expeced opion reurns as ER ( ) = r + [ MRET r ] β P P jq,, f, q q, f, q jq, ER ( ) = r + [ MRET r ] β C C jq,, f, q q, f, q jq, (9) (10) 41
P C where ER ( ) and ( ) are, respecively, he expeced reurn on a pu and call for firm in jq,, ER jq,, quarer q, measured on day, which is 30 rading days prior o he acual announcemen. The risk-free ineres rae in quarer q, r f, q, is proxied by he 3-monh Treasury bill rae available P C from he Federal Reserve websie, and β jq, and β jq, are he pu and call opion beas obained from equaions (7) and (8) for quarer q. I compue he expeced daily opion reurns in equaions (9) and (10) for each opion in my sample using he moneyness caegories and crieria defined previously. Abnormal reurns for firm j in quarer q on day are compued daily for OTM and ATM opions as AR = R E( R ) P P P jq,, jq,, jq,, C C C jq,, jq,, jq,, (11) AR = R E( R ) (12) P P where AR jq,, and AR jq,, are respecively, he abnormal reurn on a pu and call for firm in P quarer q, measured on day, which is 30 rading days prior o he acual announcemen. R jq,, is C he acual reurn on a pu opion for firm in quarer q, on day, and R jq,, is he acual reurn on a call opion for firm in quarer q, on day. I consider OTM, ATM, and ITM opions separaely because I wan o see if here is some addiional reurn ha we can generae from he higher leverage provided by OTM opions relaive o ATM or ITM opions. As in previous secions, he enire analysis in his secion is repeaed using my alernaive P measures, and C. The process is hen repeaed for each measure,, P φσ jq,, and φσ jq,, C φσ jq,, φσ jq,, BKM jq,, soring 20, 10, and 3 rading days prior o he acual earnings announcemen. Pu-Call Pariy The pu-call pariy relaion shows ha he value of a European call opion wih a cerain srike price and exercise dae can be deduced from he value of a European pu opion wih he same srike price and exercise dae, and vice versa. If his heoreical relaion does no hold, hen arbirage opporuniies may exis. The heoreical relaion beween socks, calls, and pus is given by: 42
0 r f S = c+ Ke p τ (13) where S 0 is he curren sock price, c is he value of a European call opion o buy one share, p is he value of a European pu opion o sell one share, τ is he ime o expiraion of he opion, K is he srike price of he opions, and r f is he coninuously compounded risk-free rae of ineres for an invesmen mauring in ime τ. 23 Similar o my analysis for individual socks, each quarer, a 30 rading days prior o he acual earnings announcemen, I sor socks ino quiniles based on. I use he pu-call pariy relaion o form zero-cos porfolios of opions and sock for firms in he high and low implied volailiy skew quiniles. Specifically, I shor he sock and shor a pu on he sock 30 days before he earnings announcemen and use he proceeds o purchase a call on he sock and inves he remaining cash a he risk free rae. The posiion is hen closed he day afer he earnings announcemen. This gives me a zero-cos sraegy. If he opions marke anicipaes he direcion of he earnings surprise, and if he sock marke does no anicipae he surprise, hen invesors should be able o make money wih his sraegy. However, even hough here may be informaion in he opions marke ha is no in he sock marke, i is possible ha my zero-cos porfolios do no generae abnormal reurns because of he consrain of pu-call pariy or he bidask spread. If I do no find abnormal reurns o my zero-cos porfolios, hen his suggess ha even hough opion prices may have already adjused in expecaion of an earnings surprise, i canno be aken advanage of. BKM jq,, As in previous secions, he analysis in his secion is repeaed using he alernaive P C measures and. The enire process is hen repeaed for each of my measures, BKM jq,, φσ jq,, announcemen. P C, and soring 20, 10, and 3 rading days prior o he acual earnings φσ jq,, φσ jq,, φσ jq,, 23 Pu-call pariy holds only for European opions and my opions are American. Thus, equaion (7) does no hold exacly. However, i is sill possible o use equaion (7) as an approximaion and, hence, an indicaor of rading profis. 43
Resuls Table 9 repors he percenage of earnings surprises which are posiive afer dividing he sample ino quiniles according o he call IV difference (Panel A), pu IV difference (Panel B), and BKM (Panel C). Panel A shows ha 30 days before he earnings announcemen, high call IV difference firms are less likely o have a posiive earnings surprise han low call IV difference firms (-.016). If informaion abou earnings announcemen surprises is correcly impounded ino opion prices prior o he announcemen via he implied volailiy skew, hen my expecaion is ha high call IV difference firms will have higher fuure reurns relaive o low call IV difference firms. However, he relaionship in Panel A is in he opposie direcion of wha I anicipaed and is marginally significan. In addiion, he difference beween high and low groups is economically small (1.6%). Therefore, call IV differences canno be used o reliably predic posiive earnings surprises. Panel B shows ha when measuring 20 or 30 days ou, high pu IV difference firms are more likely o have a posiive earnings surprise. Again, his relaionship is in he opposie direcion of wha I anicipaed and shows low magniude and significance. From his resul, i seems ha pu IV differences canno be used o predic negaive earnings surprises. Finally, he resuls in Panel C sugges ha if measured 10, 20 or 30 days ou, hen low BKM firms are more likely o have a posiive earnings surprise han high BKM firms. This relaionship is also in he opposie direcion of wha I anicipaed and he level of saisical significance is srong (1%). This is no easily explained given my hypohesis. Therefore, BKM does no predic earnings surprises. However, I can sill make use of he informaion conained in he volailiy skew as proxied by BKM by using i o predic fuure sock and opion reurns. Table 10 repors mean and median values and significance levels for differences beween high and low call IV difference quiniles and beween high and low pu IV difference quiniles. This is done for earnings surprise, raw sock reurns, abnormal sock reurns, raw opion reurns, abnormal opion reurns, and raw sock minus raw opion reurns. Panel A repors resuls saring 3 days before earnings announcemen. The mean resuls show almos no significan differences for anyhing beween he high and low groups. This migh be evidence of sock and opion marke efficiency. However, he median resuls for OTM pus show negaive and significan raw opion reurn and abnormal opion reurn differences. In paricular, OTM pus in low pu IV difference quiniles show greaer median abnormal reurns hen OTM pus in high pu 44
IV difference quiniles (-.0154). Raw reurn differences for OTM pus show a similar resul (-.0238). This is conrary o my expecaions if he opion marke is correcly anicipaing fuure firm performance. Tha is, opion reurns o pus in high pu IV difference quiniles should be greaer han opion reurns o pus in low pu IV difference quiniles since high pu IV difference quiniles should conain bad news abou fuure earnings. Panel B displays resuls saring 10 days ou and shows ha raw reurn and abnormal reurn differences o socks and ITM calls are higher for high call IV difference firms. This is in agreemen wih my expecaion ha a higher level of he call volailiy skew predics sronger fuure performance. However, his resul is marginally significan for socks a 10 days ou is no presen 3, 20, or 30 days ou, providing furher evidence of sock marke efficiency. Panel C repors resuls saring 20 days ou and shows ha mean and median raw and abnormal reurn differences for OTM calls are higher for low call IV difference firms. Unforunaely, given my hypohesis, his relaionship is in he wrong direcion since low call IV difference firms should show lower fuure reurns. Mean and median raw and abnormal opion reurns for OTM pus are higher for low pu IV difference firms, which is conrary o he expecaion ha pu IV differences are able o correcly forecas fuure firm performance. Finally, Panel D also shows ha 30 days before earnings announcemens mean and median raw and abnormal reurns for OTM pus are higher for low pu IV difference firms. Again, his is in conflic wih he idea ha pu IV differences can be used o correcly forecas fuure firm performance. Table 11 is similar o Table 10 excep ha i repors mean and median values and significance levels for differences beween high and low BKM quiniles. Panel A shows ha 3 days before earnings announcemens, high BKM firms have higher earnings surprises as well as higher raw and abnormal sock reurns. This suggess ha informaion abou earnings surprise is no in socks 3 days before he earnings announcemen. For pu opions, mean raw and abnormal reurns across all moneyness caegories are higher for low BKM firms and highly significan. This agrees wih my expecaions since low levels of he volailiy skew should forecas lower fuure sock reurns. The median raw and abnormal reurns o ITM pus suppor his wih period reurn differences of -.0256 and -.0206, respecively, and hese are significan a he 1% level. Panel B shows ha a 10 days ou, raw reurns for ITM call opions are higher for high BKM firms (a difference of.0122) and significan a he 5% level, which provides more suppor for he abiliy of BKM o correcly forecas fuure firm performance. In addiion, raw reurns for pu 45
opions of all moneyness caegories are higher for low BKM firms, and abnormal reurns o ITM pu opions are higher for low BKM firms. This agrees wih my expecaions and furher demonsraes he abiliy of BKM o correcly forecas fuure sock performance. Panel C shows resuls 20 days ou when mean raw reurns for ITM and OTM call opions are higher for high BKM firms. Median abnormal reurns for OTM call opions are also higher for high BKM firms (a difference of.0042) and highly significan. As in Panel B, mean raw reurns for pu opions of all moneyness caegories are higher for low BKM firms, which is again wha I expec if BKM is able o forecas fuure firm performance correcly. In addiion, mean abnormal reurns o ATM pu opions are also higher for low BKM firms. Median raw reurns for ITM pus show a similar resul, wih pu reurns o low BKM firms ouperforming pu reurns o high BKM firms by a difference of.0220. Panel D shows resuls 30 days ou where raw sock reurns are higher for high BKM firms (.0106 for mean reurns and.0090 for median reurns). In addiion, mean raw reurns for call opions of all moneyness caegories are significanly higher for high BKM firms. A similar resuls is observed for median reurns wih a significan raw reurn difference of.0022 o OTM call opions in he high BKM quinile. Abnormal reurns on OTM call opions are also higher for high BKM, firms bu only marginally significan. The mean raw and abnormal reurns o pu opions of all moneyness caegories are higher for low BKM firms and highly significan. This is also rue for median raw and abnormal reurns o ITM pus. Thus, when considering pu opions of all moneyness caegories, he resuls for 3, 10, 20, and 30 days ou, sugges ha invesors would be beer off buying pus in low BKM firms 3, 10, 20, or even 30 days before earnings announcemens. For example, 30 days before he earnings announcemen, an invesor ha iniiaes a long OTM pu posiion using opions on firms in he low BKM quinile would ouperform a similar long posiion in firms in he high BKM quinile by.0174. The raw reurn o pus is always greaer for low BKM firms and he mean difference increases o.0242 a 10 days ou, and.0532 a 3 days ou. In Tables 12 and 13 I reproduce he resuls of Tables 10 and 11, respecively, bu in a forma ha highlighs any poenial ime effecs. In each panel, resuls are presened for he periods from 3, 10, 20, and 30 days prior o he earnings announcemen unil one day afer he earnings announcemen. Since my hypohesis is ha informaion abou earnings announcemen surprises is refleced in opion prices before i is refleced in sock prices, I expec o see 46
evidence of significan abnormal reurns o opions vanishing before significan abnormal reurns vanish for socks. Overall, I find lile evidence of his in Table 12. A 10 days ou, Panel A shows higher mean abnormal reurns o socks and opions in he high call IV difference quinile relaive o he low call IV difference quinile, bu significan reurn differences are no presen a 3, 20, or 30 days ou. Panel C does show ha significan median abnormal reurns o opions vanish before median abnormal reurns o socks do, bu he significan reurn differences are only presen 20 days ou for OTM calls and 10 days ou for sock. In addiion, Panel F shows he opposie effec, where significan median abnormal reurns o OTM pus are sill presen a 3 days ou bu are no longer presen for socks. Therefore, overall here is no discernable paern o he appearance and disappearance of abnormal reurns o eiher socks or opions and, hence, here is lile suppor for he abiliy of IV difference o predic fuure firm performance. Table 13 provides some evidence of ime effecs. All panels show ha a 3 days ou, high BKM firms have higher earning surprises, and his effec is no presen furher away from expiraion. Panel A shows ha for ITM calls, high BKM firms have higher mean raw opion reurns as he earnings announcemen dae approaches. This is wha is expeced if high BKM firms correcly forecas fuure firm performance. However, his rend ends afer 10 days ou and reurns are no longer significan a 3 days ou. A 30 days ou, high BKM firms have higher raw opion reurns for ATM and OTM call opions (Panels B and C, respecively). Bu, he difference loses significance as he earnings announcemen dae nears and becomes negaive (bu no significan). Median raw and abnormal opion reurns for OTM calls in Panel C are consisenly higher for high BKM firms relaive o low BKM firms. In addiion, addiional suppor for he idea ha informaion abou fuure firm performance is conained in BKM is given by Panels D, E, and F. These panels show ha for all pu opions and all ime periods, mean raw and abnormal opion reurns are higher for low BKM firms. Again, his highlighs he possibiliy of invesors profiing from long pu posiions iniiaed in low BKM firms prior o he earnings announcemen dae. The resuls for median raw and abnormal opion reurns in Panel D are similar o he mean resuls and, herefore, also suppor his idea. Tables 14 and 15 repor reurns o pu-call pariy porfolios for differences beween high and low IV difference quiniles for ATM opions only. If he opions marke anicipaes he direcion of he earnings surprise, and if he sock marke does no anicipae he surprise, hen invesors should be able o make money wih his sraegy. In Table 14, Panels A, B, C, and D, 47
respecively, presen resuls for he periods from hree, en, weny, and hiry days prior o he earnings announcemen unil one day afer he earnings announcemen. Panel B shows significan mean and median abnormal reurn differences o high and low pu IV difference quiniles a 10 days ou. The only oher significan abnormal reurns appear in Panel D, where median abnormal reurns o he pu-call pariy porfolios for low BKM firms ouperform hose in he high BKM quinile (a difference of.0070). Table 15 reproduces he resuls of Table 14 in a forma ha highlighs any poenial ime effecs. Clearly, no discernable paern o he few significan abnormal reurns exiss. This migh be evidence of sock and opion marke efficiency and suggess ha even hough opion prices may have already adjused in expecaion of an earnings surprise, i canno be aken advanage of. Table 16 repors mean and median raw and abnormal reurns and significance levels for each ime period. Panel A displays mean (median) raw reurns for each ime period obained by calculaing he mean (median) raw reurn for each firm over he respecive ime period and hen averaging mean (median) raw reurns across firms. Panel B displays mean (median) abnormal reurns for each ime period calculaed in a similar fashion. In Panel A, mean and median raw sock reurns are always significan and posiive, which is wha I would expec given ha he marke generally rends upward over ime. However, i is also clear ha mean (median) raw sock reurns for he period from -3 o 1 make up more han 67% (53%) of he reurns in he period from -30 o 1. This suggess, ha here are highly posiive reurns around earnings announcemens and smaller posiive reurns during oher imes. This is no surprising since Table 9 clearly shows ha approximaely 80% of earnings surprises are posiive. In keeping wih he idea ha reurns are higher around earnings announcemens, Panel B shows ha mean abnormal sock reurns are posiive and significan in he (-3,1) window, negaive and insignifican in he (-10,1) window, and negaive and significan in he (-20,1) and (-30,1) windows. A similar resuls is observed for median abnormal sock reurns. This provides an explanaion for he opion reurns. Since posiive sock reurns are higher around earnings announcemens, invesors will make (lose) more on a per day invesed basis wih call (pu) opions if hey inves a day -3 hrough day 1 han if hey inves a day -10 hrough day 1. This rend coninues for he (-20,1) and (-30,1) windows. In summary, he resuls for Table 16 sugges ha since reurns are more posiive near earnings announcemens, invesors will be beer 48
offer buying calls near earnings announcemens raher han farher away. Similarly, when he resuls for pus in Table 16 are considered ogeher wih he resuls for pus in Table 11, we learn ha since reurns are more posiive near earnings announcemens, invesors will be beer off buying pus farher away from earnings announcemens. Table 17 repors mean and median raw and abnormal reurns and significance levels for each ime period afer dividing he sample ino quiniles by implied volailiy. The difference in mean raw sock reurns for high and low implied volailiy groups in Panel A ends o decrease as he earnings announcemen dae approaches and loses significance a 10 days ou. Panel A also shows ha mean raw reurns for low implied volailiy pus of all moneyness caegories are higher hen mean raw reurns for high implied volailiy pus. A similar paern is observed for mean abnormal reurns o pus in Panel B. Since high implied volailiy firms are expeced o have higher fuure sock reurns, he resuls are as anicipaed. 49
TABLE 9: Percenage of Posiive Earnings Announcemen Surprises This able repors he percenage of earnings surprises which are posiive afer dividing he sample ino quiniles according o he implied volailiy difference beween OTM and ITM call opions (call IV difference), pu IV difference, and BKM. In Panel A he sample is divided according o call IV difference quiniles. In Panel B he sample is divided according o pu IV difference quiniles. In Panel C he sample is divided according o BKM quiniles. Also presened in each panel are high minus low quiniles and significance levels. In each panel, Day represens he number of days prior o he earnings announcemen for calculaion of IV difference and BKM. Panel A: Call IV Difference Quinile Low 2 3 4 High High - Low -3 0.798 0.805 0.808 0.796 0.803 0.005 Day -10 0.768 0.785 0.793 0.776 0.778 0.010-20 0.798 0.795 0.804 0.790 0.791-0.007-30 0.791 0.810 0.805 0.808 0.775-0.016 * Panel B: Pu IV Difference Quinile Low 2 3 4 High High - Low -3 0.794 0.812 0.812 0.804 0.786-0.008 Day -10 0.767 0.793 0.790 0.786 0.764-0.003-20 0.776 0.793 0.807 0.810 0.792 0.016 * -30 0.780 0.806 0.807 0.795 0.800 0.021 ** Panel C: BKM Quinile Low 2 3 4 High High - Low -3 0.806 0.823 0.842 0.806 0.796-0.010 Day -10 0.805 0.809 0.802 0.789 0.761-0.045 *** -20 0.815 0.823 0.813 0.807 0.777-0.038 *** -30 0.814 0.827 0.822 0.812 0.771-0.043 *** * is significan a he 10% level, ** is significan a he 5% level, *** is significan a he 1% level 50
TABLE 10: Sock and Opion Reurns by IV Difference Quiniles This able repors mean and median values and significance levels for differences beween high and low call IV difference quiniles, and high and low pu IV difference quiniles for earnings surprise, raw sock reurns, abnormal sock reurns, raw opion reurns, abnormal opion reurns, and raw sock minus raw opion reurns. Daily abnormal sock reurns in each quinile are calculaed as he difference beween he sock s acual reurn and expeced reurn, as esimaed by he marke model. Average abnormal reurns in each quinile are hen compued. Daily abnormal reurns o opions are compued as he difference beween he opion s acual reurn and expeced reurn as esimaed using he opions bea and he CAPM. Average abnormal reurns for opions in each quinile are hen compued. In each panel resuls are presened for calls and pus of hree moneyness caegories, in-he-money (ITM), a-he-money (ATM), and ou-of-he-money (OTM). For call opions he sample is divided ino quiniles based on call IV difference and for pu opions he sample is divided ino quiniles based on pu IV difference. In Panel A, resuls are presened for he period from hree days prior o he earnings announcemen unil one day afer he earnings anno weny, and hiry days prior o he earnings announcemen unil one day afer he earnings announcemen. Panel A: (-3,1) Earning Surprise Raw Sock Reurn Abnormal Sock Reurn Raw Opion Reurn Abnormal Opion Reurn Sock - Opion Mean Median Mean Median Mean Median Mean Median Mean Median Mean Median Call ITM 0.0236-0.0010-0.0015-0.0037 0.0007 0.0004 0.0100 0.0090 0.0071 0.0087-0.0114 * -0.0040 Call ATM - - - - - - 0.0021 0.0133 0.0003 0.0057-0.0036-0.0057 Call OTM - - - - - - -0.0086 0.0082-0.0113-0.0048 0.0071-0.0084 Pu ITM -0.0245-0.0052 ** 0.0001 0.0018-0.0005 0.0005 0.0018-0.0086 0.0049-0.0080-0.0017 0.0030 Pu ATM - - - - - - -0.0037-0.0150 * 0.0014-0.0072 0.0037 0.0086 Pu OTM - - - - - - -0.0096-0.0238 *** -0.0069-0.0154 *** 0.0097 0.0197 *** Panel B: (-10,1) Earning Surprise Raw Sock Reurn Abnormal Sock Reurn Raw Opion Reurn Abnormal Opion Reurn Sock - Opion Mean Median Mean Median Mean Median Mean Median Mean Median Mean Median Call ITM -0.0233 0.0009 0.0065 * 0.0026 0.0079 *** 0.0041 ** 0.0136 *** 0.0020 0.0117 *** 0.0029 * -0.0071 * -0.0013 Call ATM - - - - - - 0.0104 0.0090 *** 0.0091-0.0002-0.0038-0.0028 Call OTM - - - - - - 0.0087 0.0063 * 0.0065-0.0014-0.0022-0.0039 Pu ITM -0.0104-0.0042-0.0073 ** -0.0063 *** -0.0050-0.0039 ** 0.0120 *** 0.0043 * 0.0120 *** 0.0047 ** -0.0194 *** -0.0106 ** Pu ATM - - - - - - 0.0094 * 0.0059 0.0126 ** 0.0045 ** -0.0167 ** -0.0135 ** Pu OTM - - - - - - 0.0005 0.0000 0.0037-0.0003-0.0079-0.0062 51
TABLE 10 con. Panel C: (-20,1) Earning Surprise Raw Sock Reurn Abnormal Sock Reurn Raw Opion Reurn Abnormal Opion Reurn Sock - Opion Mean Median Mean Median Mean Median Mean Median Mean Median Mean Median Call ITM -0.0208 0.0004-0.0021-0.0022-0.0016 0.0016 0.0002-0.0027 0.0001-0.0017-0.0023-0.0034 * Call ATM - - - - - - -0.0037 0.0000-0.0053-0.0029 0.0016 0.0020 Call OTM - - - - - - -0.0108 ** -0.0041 *** -0.0122 *** -0.0053 *** 0.0087 * 0.0048 * Pu ITM 0.0024-0.0013-0.0070 * -0.0017 * -0.0065 * -0.0037 0.0022 0.0016 0.0023 0.0022-0.0092-0.0001 Pu ATM - - - - - - -0.0001 0.0000-0.0017 0.0030-0.0069-0.0042 Pu OTM - - - - - - -0.0089 ** -0.0048 *** -0.0123 *** -0.0016 *** 0.0019 0.0005 Panel D: (-30,1) Earning Surprise Raw Sock Reurn Abnormal Sock Reurn Raw Opion Reurn Mean Median Mean Median Mean Median Mean Median Abnormal Opion Reurn Sock - Opion Mean Median Mean Median Call ITM -0.0187-0.0022 0.0024 0.0022 0.0016 0.0020 0.0005-0.0011 0.0006-0.0003 0.0019-0.0005 Call ATM - - - - - - 0.0003 0.0023 ** 0.0005 0.0017 0.0021 0.0014 Call OTM - - - - - - -0.0036 0.0000-0.0040-0.0020 0.0060 0.0012 Pu ITM -0.0123-0.0008 0.0007-0.0004 0.0020 0.0006 0.0021-0.0016-0.0002-0.0007-0.0014 0.0017 Pu ATM - - - - - - -0.0020 0.0000-0.0057-0.0012 ** 0.0027 0.0017 Pu OTM - - - - - - -0.0118 *** 0.0000 *** -0.0165 *** -0.0044 *** 0.0125 * 0.0076 *** * is significan a he 10% level, ** is significan a he 5% level, *** is significan a he 1% level 52
TABLE 11: Sock and Opion Reurns by BKM Difference Quiniles This able repors mean and median values and significance levels for differences beween high and low BKM quiniles for earnings surprise, raw sock reurns, abnormal sock reurns, raw opion reurns, abnormal opion reurns, and raw sock minus raw opion reurns. Daily abnormal sock reurns in each quinile are calculaed as he difference beween he sock s acual reurn and expeced reurn, as esimaed by he marke model. Average abnormal reurns in each quinile are hen compued. Daily abnormal reurns o opions are compued as he difference beween he opion s acual reurn and expeced reurn as esimaed using he opions bea and he CAPM. Average abnormal reurns for opions in each quinile are hen compued. In each panel resuls are presened for calls and pus of hree moneyness caegories, in-he-money (ITM), a-he-money (ATM), and ou-of-he-money (OTM). In Panel A, resuls are presened for he period from hree days prior o he earnings announcemen unil one day afer he earnings announcemen. In Panels B, C, and D, respecively, resuls are presened for he period from en, weny, and hiry days prior o he earnings announcemen unil one day afer he earnings announcemen. Panel A: (-3,1) Earning Surprise Raw Sock Reurn Abnormal Sock Reurn Raw Opion Reurn Abnormal Opion Reurn Sock - Opion Mean Median Mean Median Mean Median Mean Median Mean Median Mean Median Call ITM 0.0872 *** 0.0171 *** 0.0079 ** 0.0068 * 0.0075 ** 0.0069 ** 0.0055 0.0079 0.0049 0.0069 0.0025-0.0084 ** Call ATM - - - - - - -0.0066 0.0171-0.0023 0.0092 0.0145-0.0138 Call OTM - - - - - - -0.0116 0.0518 *** -0.0052 0.0245 *** 0.0195-0.0391 *** Pu ITM - - - - - - -0.0292 *** -0.0256 *** -0.0251 *** -0.0206 *** 0.0371 *** 0.0312 *** Pu ATM - - - - - - -0.0429 *** -0.0025-0.0385 *** -0.0082 * 0.0508 *** 0.0120 ** Pu OTM - - - - - - -0.0532 *** 0.0091-0.0480 *** -0.0072 0.0611 *** 0.0089 ** Panel B: (-10,1) Earning Surprise Raw Sock Reurn Abnormal Sock Reurn Raw Opion Reurn Mean Median Mean Median Mean Median Mean Median Abnormal Opion Reurn Sock - Opion Mean Median Mean Median Call ITM -0.0242 0.0097 ** 0.0069 0.0072 0.0022 0.0027 0.0122 ** -0.0004 0.0056-0.0023-0.0053-0.0030 Call ATM - - - - - - 0.0026 0.0079 ** 0.0002-0.0058 0.0043 0.0006 Call OTM - - - - - - -0.0042 0.0229 *** -0.0037 0.0024 *** 0.0111-0.0173 *** Pu ITM - - - - - - -0.0203 *** -0.0125 *** -0.0116 *** -0.0057 ** 0.0272 *** 0.0223 *** Pu ATM - - - - - - -0.0201 *** 0.0056-0.0037 0.0003 0.0270 *** 0.0001 * Pu OTM - - - - - - -0.0242 *** 0.0000-0.0076 0.0007 0.0311 *** 0.0028 53
TABLE 11 con. Panel C: (-20,1) Earning Surprise Raw Sock Reurn Abnormal Sock Reurn Raw Opion Reurn Abnormal Opion Reurn Sock - Opion Mean Median Mean Median Mean Median Mean Median Mean Median Mean Median Call ITM -0.0080 0.0162 *** 0.0075 0.0073 ** -0.0013 0.0023 0.0083 ** -0.0050 0.0057 * -0.0040-0.0007 0.0030 * Call ATM - - - - - - 0.0064-0.0011 0.0054-0.0023 0.0011 0.0074 ** Call OTM - - - - - - 0.0099 * 0.0042 *** 0.0072 0.0019 *** -0.0024-0.0077 Pu ITM - - - - - - -0.0088 *** -0.0220 *** -0.0046-0.0088 *** 0.0163 *** 0.0177 *** Pu ATM - - - - - - -0.0105 *** 0.0000-0.0099 *** -0.0016 0.0180 *** 0.0004 *** Pu OTM - - - - - - -0.0109 * 0.0000-0.0093-0.0037 * 0.0185 ** 0.0053 *** Panel D: (-30,1) Earning Surprise Raw Sock Reurn Abnormal Sock Reurn Raw Opion Reurn Abnormal Opion Reurn Sock - Opion Mean Median Mean Median Mean Median Mean Median Mean Median Mean Median Call ITM -0.0150 0.0129 ** 0.0106 * 0.0090 ** 0.0074 0.0084 ** 0.0055 ** -0.0021 0.0031-0.0018 0.0050 0.0088 ** Call ATM - - - - - - 0.0076 ** 0.0000 0.0057 0.0008 * 0.0030 0.0062 Call OTM - - - - - - 0.0117 *** 0.0022 *** 0.0085 * 0.0026 *** -0.0012-0.0007 Pu ITM - - - - - - -0.0157 *** -0.0156 *** -0.0137 *** -0.0072 *** 0.0263 *** 0.0194 *** Pu ATM - - - - - - -0.0171 *** 0.0000-0.0142 ** -0.0018 0.0276 *** 0.0058 *** Pu OTM - - - - - - -0.0174 *** 0.0000-0.0157 ** -0.0024 0.0280 *** 0.0055 ** * is significan a he 10% level, ** is significan a he 5% level, *** is significan a he 1% level 54
TABLE 12: Sock and Opion Reurns by IV Difference Quiniles (Time Effecs) This able repors mean and median values and significance levels for differences beween high and low IV difference quiniles for earnings surprise, raw sock reurns, abnormal sock reurns, raw opion reurns, abnormal opions reurns, and raw sock minus raw opion reurns. Daily abnormal sock reurns in each quinile are calculaed as he difference beween he sock s acual reurn and expeced reurn, as esimaed by he marke model. Average abnormal reurns in each quinile are hen compued. Daily abnormal reurns o opions are compued as he difference beween he opion s acual reurn and expeced reurn as esimaed using he opions bea and he CAPM. Average abnormal reurns for opions in each quinile are hen compued. For call opions, he sample is divided ino quiniles based on call IV differences. For pu opions, he sample is divided ino quiniles based on pu IV differences. In Panel A, resuls are for in-he-money (ITM) call opions. In Panels B, C, D, E, and F, respecively, resuls are presened for a-he-money (ATM) call opions, ou-of-he-money (OTM) call opions, ITM pu opions, ATM pu opions, and OTM pu opions. In each panel, resulsare presened for he periods from hree, en, weny, and hiry days prior o he earnings announcemen unil one day afer he earnings announcemen. Panel A: Call ITM Earning Surprise Raw Sock Reurn Abnormal Sock Reurn Raw Opion Reurn Abnormal Opion Reurn Sock - Opion Mean Median Mean Median Mean Median Mean Median Mean Median Mean Median (-3,1) 0.0236-0.0010-0.0015-0.0037 0.0007 0.0004 0.0100 0.0090 0.0071 0.0087-0.0114 * -0.0040 (-10,1) -0.0233 0.0009 0.0065 * 0.0026 0.0079 *** 0.0041 ** 0.0136 *** 0.0020 0.0117 *** 0.0029 * -0.0071 * -0.0013 (-20,1) -0.0208 0.0004-0.0021-0.0022-0.0016 0.0016 0.0002-0.0027 0.0001-0.0017-0.0023-0.0034 * (-30,1) -0.0187-0.0022 0.0024 0.0022 0.0016 0.0020 0.0005-0.0011 0.0006-0.0003 0.0019-0.0005 Panel B: Call ATM Earning Surprise Raw Sock Reurn Abnormal Sock Reurn Raw Opion Reurn Mean Median Mean Median Mean Median Mean Median (-3,1) 0.0236-0.0010-0.0015-0.0037 0.0007 0.0004 0.0021 0.0133 0.0003 0.0057-0.0036-0.0057 (-10,1) -0.0233 0.0009 0.0065 * 0.0026 0.0079 *** 0.0041 ** 0.0104 0.0090 *** 0.0091-0.0002-0.0038-0.0028 (-20,1) -0.0208 0.0004-0.0021-0.0022-0.0016 0.0016-0.0037 0.0000-0.0053-0.0029 0.0016 0.0020 (-30,1) -0.0187-0.0022 0.0024 0.0022 0.0016 0.0020 0.0003 0.0023 ** 0.0005 0.0017 0.0021 0.0014 Panel C: Call OTM Earning Surprise Raw Sock Reurn Abnormal Sock Reurn Raw Opion Reurn Mean Median Mean Median Mean Median Mean Median Abnormal Opion Reurn Sock - Opion Mean Median Mean Median Abnormal Opion Reurn Sock - Opion Mean Median Mean Median (-3,1) 0.0236-0.0010-0.0015-0.0037 0.0007 0.0004-0.0086 0.0082-0.0113-0.0048 0.0071-0.0084 (-10,1) -0.0233 0.0009 0.0065 * 0.0026 0.0079 *** 0.0041 ** 0.0087 0.0063 * 0.0065-0.0014-0.0022-0.0039 (-20,1) -0.0208 0.0004-0.0021-0.0022-0.0016 0.0016-0.0108 ** -0.0041 *** -0.0122 *** -0.0053 *** 0.0087 * 0.0048 * (-30,1) -0.0187-0.0022 0.0024 0.0022 0.0016 0.0020-0.0036 0.0000-0.0040-0.0020 0.0060 0.0012 55
TABLE 12 con. Panel D: Pu ITM Earning Surprise Raw Sock Reurn Abnormal Sock Reurn Raw Opion Reurn Mean Median Mean Median Mean Median Mean Median (-3,1) -0.0245-0.0052 ** 0.0001 0.0018-0.0005 0.0005 0.0018-0.0086 0.0049-0.0080-0.0017 0.0030 (-10,1) -0.0104-0.0042-0.0073 ** -0.0063 *** -0.0050-0.0039 ** 0.0120 *** 0.0043 * 0.0120 *** 0.0047 ** -0.0194 *** -0.0106 ** (-20,1) 0.0024-0.0013-0.0070 * -0.0017 * -0.0065 * -0.0037 0.0022 0.0016 0.0023 0.0022-0.0092-0.0001 (-30,1) -0.0123-0.0008 0.0007-0.0004 0.0020 0.0006 0.0021-0.0016-0.0002-0.0007-0.0014 0.0017 Panel E: Pu ATM Earning Surprise Raw Sock Reurn Abnormal Sock Reurn Raw Opion Reurn Mean Median Mean Median Mean Median Mean Median Abnormal Opion Reurn Sock - Opion Mean Median Mean Median Abnormal Opion Reurn Sock - Opion Mean Median Mean Median (-3,1) -0.0245-0.0052 ** 0.0001 0.0018-0.0005 0.0005-0.0037-0.0150 * 0.0014-0.0072 0.0037 0.0086 (-10,1) -0.0104-0.0042-0.0073 ** -0.0063 *** -0.0050-0.0039 ** 0.0094 * 0.0059 0.0126 ** 0.0045 ** -0.0167 ** -0.0135 ** (-20,1) 0.0024-0.0013-0.0070 * -0.0017 * -0.0065 * -0.0037-0.0001 0.0000-0.0017 0.0030-0.0069-0.0042 (-30,1) -0.0123-0.0008 0.0007-0.0004 0.0020 0.0006-0.0020 0.0000-0.0057-0.0012 ** 0.0027 0.0017 Panel F: Pu OTM Earning Surprise Raw Sock Reurn Abnormal Sock Reurn Raw Opion Reurn Mean Median Mean Median Mean Median Mean Median Abnormal Opion Reurn Sock - Opion Mean Median Mean Median (-3,1) -0.0245-0.0052 ** 0.0001 0.0018-0.0005 0.0005-0.0096-0.0238 *** -0.0069-0.0154 *** 0.0097 0.0197 *** (-10,1) -0.0104-0.0042-0.0073 ** -0.0063 *** -0.0050-0.0039 ** 0.0005 0.0000 0.0037-0.0003-0.0079-0.0062 (-20,1) 0.0024-0.0013-0.0070 * -0.0017 * -0.0065 * -0.0037-0.0089 ** -0.0048 *** -0.0123 *** -0.0016 *** 0.0019 0.0005 (-30,1) -0.0123-0.0008 0.0007-0.0004 0.0020 0.0006-0.0118 *** 0.0000-0.0165 *** -0.0044 *** 0.0125 * 0.0076 *** * is significan a he 10% level, ** is significan a he 5% level, *** is significan a he 1% level 56
TABLE 13: Sock and Opion Reurns by BKM Difference Quiniles (Time Effecs) This able repors mean and median values and significance levels for differences beween high and low BKM quiniles for earnings surprise, raw sock reurns, abnormal sock reurns, raw opion reurns, abnormal opions reurns, and raw sock minus raw opion reurns. Daily abnormal sock reurns in each quinile are calculaed as he difference beween he sock s acual reurn and expeced reurn, as esimaed by he marke model. Average abnormal reurns in each quinile are hen compued. Daily abnormal reurns o opions are compued as he difference beween he opion s acual reurn and expeced reurn as esimaed using he opions bea and he CAPM. Average abnormal reurns for opions in each quinile are hen compued. In Panel A, resuls are for in-he-money (ITM) call opions. In Panels B, C, D, E, and F, respecively, resuls are presened for a-he-money (ATM) call opions, ou-of-he-money (OTM) call opions, ITM pu opions, ATM pu opions, and OTM pu opions. In each panel, resuls are presened for he periods from hree, en, weny, and hiry days prior o he earnings announcemen unil one day afer he earnings announcemen. Panel A: Call ITM Earning Surprise Raw Sock Reurn Abnormal Sock Reurn Raw Opion Reurn Abnormal Opion Reurn Sock - Opion Mean Median Mean Median Mean Median Mean Median Mean Median Mean Median (-3,1) 0.0872 *** 0.0171 *** 0.0079 ** 0.0068 * 0.0075 ** 0.0069 ** 0.0055 0.0079 0.0049 0.0069 0.0025-0.0084 ** (-10,1) -0.0242 0.0097 ** 0.0069 0.0072 0.0022 0.0027 0.0122 ** -0.0004 0.0056-0.0023-0.0053-0.0030 (-20,1) -0.0080 0.0162 *** 0.0075 0.0073 ** -0.0013 0.0023 0.0083 ** -0.0050 0.0057 * -0.0040-0.0007 0.0030 * (-30,1) -0.0150 0.0129 ** 0.0106 * 0.0090 ** 0.0074 0.0084 ** 0.0055 ** -0.0021 0.0031-0.0018 0.0050 0.0088 ** Panel B: Call ATM Earning Surprise Raw Sock Reurn Abnormal Sock Reurn Raw Opion Reurn Abnormal Opion Reurn Sock - Opion Mean Median Mean Median Mean Median Mean Median Mean Median Mean Median (-3,1) 0.0872 *** 0.0171 *** 0.0079 ** 0.0068 * 0.0075 ** 0.0069 ** -0.0066 0.0171-0.0023 0.0092 0.0145-0.0138 (-10,1) -0.0242 0.0097 ** 0.0069 0.0072 0.0022 0.0027 0.0026 0.0079 ** 0.0002-0.0058 0.0043 0.0006 (-20,1) -0.0080 0.0162 *** 0.0075 0.0073 ** -0.0013 0.0023 0.0064-0.0011 0.0054-0.0023 0.0011 0.0074 ** (-30,1) -0.0150 0.0129 ** 0.0106 * 0.0090 ** 0.0074 0.0084 ** 0.0076 ** 0.0000 0.0057 0.0008 * 0.0030 0.0062 Panel C: Call OTM Earning Surprise Raw Sock Reurn Abnormal Sock Reurn Raw Opion Reurn Abnormal Opion Reurn Sock - Opion Mean Median Mean Median Mean Median Mean Median Mean Median Mean Median (-3,1) 0.0872 *** 0.0171 *** 0.0079 ** 0.0068 * 0.0075 ** 0.0069 ** -0.0116 0.0518 *** -0.0052 0.0245 *** 0.0195-0.0391 *** (-10,1) -0.0242 0.0097 ** 0.0069 0.0072 0.0022 0.0027-0.0042 0.0229 *** -0.0037 0.0024 *** 0.0111-0.0173 *** (-20,1) -0.0080 0.0162 *** 0.0075 0.0073 ** -0.0013 0.0023 0.0099 * 0.0042 *** 0.0072 0.0019 *** -0.0024-0.0077 (-30,1) -0.0150 0.0129 ** 0.0106 * 0.0090 ** 0.0074 0.0084 ** 0.0117 *** 0.0022 *** 0.0085 * 0.0026 *** -0.0012-0.0007 57
TABLE 13 con. Panel D: Pu ITM Earning Surprise Raw Sock Reurn Abnormal Sock Reurn Raw Opion Reurn Abnormal Opion Reurn Sock - Opion Mean Median Mean Median Mean Median Mean Median Mean Median Mean Median (-3,1) 0.0872 *** 0.0171 *** 0.0079 ** 0.0068 * 0.0075 ** 0.0069 ** -0.0292 *** -0.0256 *** -0.0251 *** -0.0206 *** 0.0371 *** 0.0312 *** (-10,1) -0.0242 0.0097 ** 0.0069 0.0072 0.0022 0.0027-0.0203 *** -0.0125 *** -0.0116 *** -0.0057 ** 0.0272 *** 0.0223 *** (-20,1) -0.0080 0.0162 *** 0.0075 0.0073 ** -0.0013 0.0023-0.0088 *** -0.0220 *** -0.0046-0.0088 *** 0.0163 *** 0.0177 *** (-30,1) -0.0150 0.0129 ** 0.0106 * 0.0090 ** 0.0074 0.0084 ** -0.0157 *** -0.0156 *** -0.0137 *** -0.0072 *** 0.0263 *** 0.0194 *** Panel E: Pu ATM Earning Surprise Raw Sock Reurn Abnormal Sock Reurn Raw Opion Reurn Mean Median Mean Median Mean Median Mean Median Abnormal Opion Reurn Sock - Opion Mean Median Mean Median (-3,1) 0.0872 *** 0.0171 *** 0.0079 ** 0.0068 * 0.0075 ** 0.0069 ** -0.0429 *** -0.0025-0.0385 *** -0.0082 * 0.0508 *** 0.0120 ** (-10,1) -0.0242 0.0097 ** 0.0069 0.0072 0.0022 0.0027-0.0201 *** 0.0056-0.0037 0.0003 0.0270 *** 0.0001 * (-20,1) -0.0080 0.0162 *** 0.0075 0.0073 ** -0.0013 0.0023-0.0105 *** 0.0000-0.0099 *** -0.0016 0.0180 *** 0.0004 *** (-30,1) -0.0150 0.0129 ** 0.0106 * 0.0090 ** 0.0074 0.0084 ** -0.0171 *** 0.0000-0.0142 ** -0.0018 0.0276 *** 0.0058 *** Panel F: Pu OTM Earning Surprise Raw Sock Reurn Abnormal Sock Reurn Raw Opion Reurn Mean Median Mean Median Mean Median Mean Median Abnormal Opion Reurn Sock - Opion Mean Median Mean Median (-3,1) 0.0872 *** 0.0171 ** 0.0079 ** 0.0068 * 0.0075 ** 0.0069 ** -0.0532 *** 0.0091-0.0480 *** -0.0072 0.0611 *** 0.0089 ** (-10,1) -0.0242 0.0097 ** 0.0069 0.0072 0.0022 0.0027-0.0242 *** 0.0000-0.0076 0.0007 0.0311 *** 0.0028 (-20,1) -0.0080 0.0162 *** 0.0075 0.0073 ** -0.0013 0.0023-0.0109 * 0.0000-0.0093-0.0037 * 0.0185 ** 0.0053 *** (-30,1) -0.0150 0.0129 ** 0.0106 * 0.0090 ** 0.0074 0.0084 ** -0.0174 *** 0.0000-0.0157 ** -0.0024 0.0280 *** 0.0055 ** * is significan a he 10% level, ** is significan a he 5% level, *** is significan a he 1% level 58
TABLE 14: Reurns o Pu-Call Pariy Porfolios This able repors reurns o pu-call pariy porfolios for differences beween high and low IV difference quiniles and high and low BKM quiniles for ATM opions only. To obain he reurns in Panel A, we shor he sock and shor a pu on he sock hree days before he earnings announcemen and use he proceeds o purchase a call on he sock and inves he remaining cash a he risk free rae. The posiion is hen closed he day afer he earnings announcemen. We compue he dollar value of reurns o his sraegy and sandardize i in wo differen ways; our firs mehod divides by he sock price a he ime he posiion was iniiaed, our second mehod divides by he call price a he ime he posiion was iniiaed. In Panels B, C, and D, respecively, resuls are presened for he periods from en, weny, and hiry days prior o he earnings announcemen unil one day afer he earnings announcemen. Panel A: (-3,1) Call IV Quiniles 0.0018 0.0024 0.0738 0.0836 Pu IV Quiniles -0.0001-0.0001 0.0385-0.0457 BKM Quiniles -0.0046-0.0037 0.1291-0.0388 Panel B: (-10,1) Call IV Quiniles -0.0061 * -0.0028-0.2010-0.0963 Pu IV Quiniles 0.0065 ** 0.0058 *** 0.2298 0.1661 *** BKM Quiniles -0.0049-0.0052 0.3013-0.0295 Panel C: (-20,1) Call IV Quiniles 0.0019 0.0033-0.0269 0.1130 Pu IV Quiniles 0.0067 * 0.0013 * 0.2311 0.0063 BKM Quiniles -0.0060-0.0050 * 0.2100-0.0547 Panel D: (-30,1) Zero Cos/Sock Price Zero Cos/Call Price Mean Median Mean Median Zero Cos/Sock Price Zero Cos/Call Price Mean Median Mean Median Zero Cos/Sock Price Zero Cos/Call Price Mean Median Mean Median Zero Cos/Sock Price Zero Cos/Call Price Mean Median Mean Median Call IV Quiniles -0.0023-0.0019-0.0480-0.0442 Pu IV Quiniles -0.0006 0.0002-0.3705 * -0.0043 BKM Quiniles -0.0093 * -0.0070 ** 0.2043-0.1242 * is significan a he 10% level, ** is significan a he 5% level, *** is significan a he 1% level 59
TABLE 15: Reurns o Pu-Call Pariy Porfolios (Time Effecs) This able repors reurns o pu-call pariy porfolios for differences beween high and low IV difference quiniles and high and low BKM quiniles for ATM opions only. In each panel, resuls are presened for he periods from hree, en, weny, and hiry days prior o he earnings announcemen unil one day afer he earnings announcemen. To obain he reurns in Panel A, we use socks sored by call IV difference and shor he sock and shor a pu on he sock hree days before he earnings announcemen and use he proceeds o purchase a call on he sock while invesing he remaining cash a he risk free rae. The posiion is closed he day afer he earnings announcemen. We compue he dollar value of reurns o his sraegy and sandardize i in wo differen ways; our firs mehod divides by he sock price a he ime he posiion was iniiaed, our second mehod divides by he call price a he ime he posiion was iniiaed. In Panels B, and C, respecively, resuls are presened for firms sored by pu IV difference, and for firms sored by differences beween high and low BKM quiniles. Panel A: Call IV Quiniles (-3,1) 0.0018 0.0024 0.0738 0.0836 (-10,1) -0.0061 * -0.0028-0.2010-0.0963 (-20,1) 0.0019 0.0033-0.0269 0.1130 (-30,1) -0.0023-0.0019-0.0480-0.0442 Panel B: Pu IV Quiniles Zero Cos/Sock Price Zero Cos/Call Price Mean Median Mean Median (-3,1) -0.0001-0.0001 0.0385-0.0457 (-10,1) 0.0065 ** 0.0058 *** 0.2298 0.1661 *** (-20,1) 0.0067 * 0.0013 * 0.2311 0.0063 (-30,1) -0.0006 0.0002-0.3705 * -0.0043 Panel C: BKM Quiniles Zero Cos/Sock Price Zero Cos/Call Price Mean Median Mean Median Zero Cos/Sock Price Zero Cos/Call Price Mean Median Mean Median (-3,1) -0.0046-0.0037 0.1291-0.0388 (-10,1) -0.0049-0.0052 0.3013-0.0295 (-20,1) -0.0060-0.0050 * 0.2100-0.0547 (-30,1) -0.0093 * -0.0070 ** 0.2043-0.1242 * is significan a he 10% level, ** is significan a he 5% level, *** is significan a he 1% level 60
TABLE 16: Raw and Abnormal Sock and Opion Reurns This able repors mean and median raw and abnormal reurns and significance levels for each ime period. Panel A displays mean raw reurns for each ime period obained by calculaing he mean raw reurn for each firm over he respecive ime period and hen averaging mean raw reurns across firms. Panel B displays mean abnormal reurns for each ime period obained by calculaing he mean abnormal reurn for each firm over he respecive ime period and hen averaging mean abnormal reurns across firms. Panel A: Raw Reurns (-3,1) (-10,1) (-20,1) (-30,1) Mean Median Mean Median Mean Median Mean Median Sock 0.0119 *** 0.0116 *** 0.0151 *** 0.0154 *** 0.0172 *** 0.0192 *** 0.0176 *** 0.0217 *** CITM 0.0243 *** -0.0143 *** 0.0130 *** -0.0198 *** -0.0003-0.0238 *** -0.0026 *** -0.0213 *** CATM 0.0333 *** -0.0518 *** 0.0157 *** -0.0563 *** -0.0068 *** -0.0612 *** -0.0079 *** -0.0500 *** COTM 0.0138 *** -0.1111 *** 0.0048 * -0.0955 *** -0.0164 *** -0.0667 *** -0.0189 *** -0.0526 *** PITM -0.0157 *** -0.0638 *** -0.0081 *** -0.0431 *** -0.0066 *** -0.0317 *** -0.0036 *** -0.0274 *** PATM -0.0201 *** -0.1000 *** -0.0126 *** -0.0777 *** -0.0119 *** -0.0625 *** -0.0090 *** -0.0500 *** POTM -0.0397 *** -0.1481 *** -0.0258 *** -0.1000 *** -0.0247 *** -0.0667 *** -0.0202 *** -0.0526 *** Panel B: Abnormal Reurns (-3,1) (-10,1) (-20,1) (-30,1) Mean Median Mean Median Mean Median Mean Median Sock 0.0038 *** 0.0050 *** -0.0015 0.0018 ** -0.0087 *** -0.0025 *** -0.0180 *** -0.0089 *** CITM 0.0165 *** -0.0195 *** 0.0065 *** -0.0181 *** -0.0034 *** -0.0202 *** -0.0057 *** -0.0186 *** CATM 0.0220 *** -0.0452 *** 0.0070 *** -0.0391 *** -0.0108 *** -0.0364 *** -0.0122 *** -0.0307 *** COTM 0.0017-0.0829 *** -0.0032-0.0530 *** -0.0194 *** -0.0442 *** -0.0232 *** -0.0371 *** PITM -0.0115 *** -0.0522 *** -0.0087 *** -0.0340 *** -0.0050 *** -0.0243 *** -0.0027 *** -0.0203 *** PATM -0.0140 *** -0.0776 *** -0.0148 *** -0.0511 *** -0.0095 *** -0.0376 *** -0.0080 *** -0.0310 *** POTM -0.0313 *** -0.1076 *** -0.0260 *** -0.0631 *** -0.0200 *** -0.0455 *** -0.0173 *** -0.0358 *** * is significan a he 10% level, ** is significan a he 5% level, *** is significan a he 1% level 61
TABLE 17: Raw and Abnormal Sock and Opion Reurns by Implied Volailiy Difference Quiniles This able repors mean and median raw and abnormal reurns and significance levels for each ime period afer dividing he sample ino quiniles by implied volailiy. Mean raw reurns in Panel A are obained as he difference in mean raw reurns for firms in he high and low implied volailiy quiniles for each corresponding ime period. Mean abnormal reurns in Panel B are obained as he difference in mean abnormal reurns for firms in he high and low implied volailiy quiniles for each corresponding ime period. Panel A: Raw Reurns (-3,1) (-10,1) (-20,1) (-30,1) Mean Median Mean Median Mean Median Mean Median Sock 0.0041 0.0101 0.0069 0.0083 0.0167 *** 0.0252 0.0267 *** 0.0318 CITM 0.0093-0.0267 0.0023-0.0249 0.0076 *** -0.0200 0.0064 * -0.0162 CATM 0.0012-0.0229-0.0142 * -0.0138 0.0062-0.0024 0.0057 0.0000 COTM 0.0205-0.0208-0.0029 0.0006 0.0111 *** 0.0000 0.0074 0.0015 PITM -0.0028-0.0247-0.0080-0.0256-0.0120 *** -0.0306-0.0035-0.0256 PATM 0.0070-0.0285-0.0163 ** -0.0182-0.0134 *** -0.0025-0.0052 0.0000 POTM 0.0268 * -0.0036-0.0148 0.0000-0.0121 ** 0.0000-0.0066 0.0000 Panel B: Abnormal Reurns (-3,1) (-10,1) (-20,1) (-30,1) Mean Median Mean Median Mean Median Mean Median Sock -0.0045 0.0024-0.0137 *** -0.0088-0.0226 *** -0.0078-0.0166 *** -0.0050 CITM 0.0048-0.0236-0.0035-0.0218 0.0038-0.0128 0.0041-0.0077 CATM -0.0008-0.0156-0.0224 *** -0.0182 0.0032-0.0044 0.0057-0.0032 COTM 0.0168-0.0036-0.0103-0.0128 0.0078 0.0004 0.0078 0.0000 PITM -0.0065-0.0205-0.0029-0.0163-0.0120 *** -0.0169-0.0052-0.0168 PATM 0.0045-0.0153-0.0005-0.0134-0.0156 *** -0.0110-0.0083-0.0095 POTM 0.0225 0.0038 0.0012-0.0029-0.0153 *** -0.0086-0.0125-0.0091 * is significan a he 10% level, ** is significan a he 5% level, *** is significan a he 1% level 62
CONCLUSION The resuls of my firs chaper show ha implied idiosyncraic volailiy from opion prices represens a beer measure (compared o hisorical realized volailiy measures) of he marke s anicipaed volailiy and provides a beer way o examine he relaion beween fuure reurns and idiosyncraic risk. I employ sock and opion prices from firms wih raded opions from 1996 hrough June, 2005. A he firm level implied idiosyncraic volailiy is an upward biased predicor of realized idiosyncraic volailiy, even in he presence of pas realized volailiy. Implied idiosyncraic volailiy is a sronger predicor of fuure idiosyncraic volailiy han idiosyncraic volailiy forecass from saisical models. I conrol for firm characerisics in a Fama-MacBeh approach and find ha implied idiosyncraic risk posiively predics fuure sock reurns while realized idiosyncraic volailiy does no. For predicing reurns, implied idiosyncraic volailiy dominaes idiosyncraic volailiy forecass from saisical models. Also, he Ofek, Richardson, and Whielaw (2004) measure of shor-sale consrains has a srong negaive effec on fuure reurns. I use porfolio analysis and four-facor regressions o show ha implied and realized idiosyncraic volailiies posiively predic fuure reurns. When I compare implied and realized idiosyncraic volailiy o each oher, however, implied idiosyncraic volailiy is posiively linked o fuure reurns bu realized idiosyncraic risk is no. This suggess ha idiosyncraic risk maers as long as i is derived from he forward measure. Conrolling for size and book-o-marke equiy, I find ha he srengh of idiosyncraic volailiy is srongly ied o small size and high book-o-marke equiy firms. Socks wih low shor-sale consrains ouperform firms wih high shor-sale consrains, bu he reurns are unrelaed o firm implied idiosyncraic volailiy. The amoun of opion open ineres is unimporan. So, implied idiosyncraic risk predics fuure reurns and zero-cos porfolios based on implied idiosyncraic risk sors lead o significan four-facor alphas. This may be indicaive of abnormal reurns or, alernaively, may mean ha idiosyncraic risk is an omied risk facor. My evidence is consisen wih prior sudies advocaing a posiive relaion beween idiosyncraic risk and fuure reurns, bu in conras o he resuls in Ang, Hodrick, Xing, and Zhang (2006). This may be direcly relaed o he informaion conen in implied volailiy, which by definiion is a forward looking measure. Realized volailiy measures are uninformaive 63
in he presence of implied volailiy measures boh for predicing fuure volailiy and reurns. Thus, my main conribuion is o provide an appropriae ex-ane measure of risk which demonsraes he posiive relaion beween risk and reurn. The main goal of my second chaper is o invesigae wheher informaion abou earnings announcemen surprises is correcly impounded ino opion prices prior o he announcemen via he implied volailiy skew. Throughou ha chaper I proxy for he implied volailiy skew wih pu IV difference, call IV difference, and BKM. The percenage of earnings surprises which are posiive afer dividing he sample ino quiniles according o he call volailiy skew shows ha 30 days before he earnings announcemen, high call IV difference firms are less likely o have a posiive earnings surprise han low call IV difference firms. This relaionship is in he opposie direcion of wha I anicipaed. A 20 or 30 days ou, high pu IV difference firms are more likely o have a posiive earnings surprise. Again, his relaionship is in he opposie direcion of wha I anicipaed. The resuls for BKM sugges a significan negaive relaionship exiss beween BKM and earnings surprises when measured 10, 20 or 30 days ou, bu his is also in he opposie direcion of wha I anicipaed. Neverheless, I can sill make use of he informaion conained in he volailiy skew as proxied by BKM. When using BKM and considering pu opions of all moneyness caegories, he resuls sugges ha invesors would be beer off buying pu opions in low volailiy skew firms 3, 10, 20, or even 30 days before earnings announcemens. This invesmen sraegy should be approached wih cauion since boh he raw and abnormal reurns o pus for low BKM firms end o decrease as he earnings announcemen dae approaches. This is likely due o he fac ha he majoriy of posiive reurns o firms occur around he earnings announcemen dae. Evidence for his is seen in Table 16 where i is clear ha raw sock reurns for he period (-3,1) make up abou 67% of he reurns in he (-30,1) period. This suggess ha here are highly posiive reurns around earnings announcemens and smaller posiive reurns during oher imes. This is no surprising since abou 80% of earnings surprises are posiive and also provides an explanaion for he opion reurns observed in Table 16. Since posiive sock reurns are higher around earnings announcemens, invesors will be beer offer buying calls near earnings announcemens raher han furher away. Similarly, since reurns are more posiive near earnings announcemens, if invesors choose o buy pus, hey will be beer off buying hem furher away from earning announcemens. 64
APPENDIX A: Expressions for Risk-Neural Skewness The model-free esimaes of risk-neural skewness are based on Bakshi, Kapadia and Madan (2003). Le (, ) log( log( ) R S τ S τ + and. BKM is defined as: )}, ( { ), ( τ τ μ R E Q ( ) 2 3 2 2 3 2 3 ), ( ), ( ), ( 3 ), ( ), ( 3 ), ( }) )), ( ), ( {( ( } )), ( ), ( {( τ μ τ ν τ μ τ ν τ μ τ τ μ τ τ μ τ τ τ τ e e W e R E R E BKM r r r Q Q + = (A.1) where, ) ; ( log 1 2 ) ; ( log 1 2 ), ( 0 2 2 dk K P K K S dk K C K S K S S τ τ τ ν + + = (A.2) and he price of he cubic and quaric conracs are (A.3) (A.4). ) ; ( log 4 log 12 ) ; ( log 4 log 12 ), (, ) ; ( log 3 6log ) ; ( log 3 6 log ), ( 0 2 3 2 2 3 2 0 2 2 2 2 dk K P K K S K S dk K C K S K S K X dk K P K K S K S dk K C K S K S K W S S S S τ τ τ τ τ τ + = + = Finally, )., ( 24 ), ( 6 ), ( 2 1 ), ( τ τ τ τ μ τ τ τ τ X e W e v e e r r r r 65
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BIOGRAPHICAL SKETCH Consanine Diavaopoulos was born in Monreal, Canada and raised in Chicago, Illinois. He holds pos-graduae degrees in Finance (Ph.D. from Florida Sae Universiy) and Saisics (M.S. from Florida Sae Universiy), and did undergraduae work in Business, Mahemaics and Compuer Science. Prior o being an academic, he worked in he fuures and opions business in Chicago. He has broad research ineress which include invesmens, derivaives, empirical asse pricing, corporae finance, and behavioral finance. 70