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1 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

2 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

3 The members of he Commiee approve he disseraion of Consanine Diavaopoulos defended on April 3, 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

4 TABLE OF CONTENTS Lis of Tables..... iv Lis of Figures..... v Absrac... vi INTRODUCTION THE INFORMATION CONTENT IN IMPLIED VOLATILITY AND THE CROSS- SECTION OF STOCK RETURNS: EVIDENCE FROM THE OPTION MARKETS OPTION MARKET EFFICIENCY AND EARNINGS ANNOUNCEMENTS.. 35 CONCLUSION APPENDIX REFERENCES.. 66 BIOGRAPHICAL SKETCH. 70 iii

5 LIST OF TABLES Table 1. Descripive Saisics of Opion Firm Sample Table 2. Forecasing Fuure Realized Volailiy Table 3. Forecasing Firm Fuure Realized Volailiy wih Idiosyncraic Volailiy Table 4. Fama-MacBeh Esimaion wih All Available Socks Table 5. Fama-MacBeh Esimaion on Socks wih Opions Table 6. Mean Values of Firm Characerisics for Sored Porfolios Table 7. Idiosyncraic Porfolio Percenage Reurns Table 8. Double-Sored High Minus Low Percenage Porfolio Reurns Table 9. Percenage of Posiive Earnings Announcemen Surprises 50 Table 10. Sock and Opion Reurns by IV Difference Quiniles Table 11. Sock and Opion Reurns by BKM Difference Quiniles 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) Table 14. Reurns o Pu-Call Pariy Porfolios Table 15. Reurns o Pu-Call Pariy Porfolios (Time Effecs) Table 16. Raw and Abnormal Sock and Opion Reurns. 61 Table 17. Raw and Abnormal Sock and Opion Reurns by Impled Volailiy Difference Quiniles iv

6 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 v

7 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

8 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

9 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 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

10 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

11 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

12 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

13 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

14 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

15 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

16 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

17 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 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 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

18 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) 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

19 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 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

20 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 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

21 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

22 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 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

23 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, 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

24 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: 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., 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 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 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

25 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 λ r AR _ idio, 5 11: 1 + λ ORW 11 + λ r 6 35: 12 λ ε _ Raio + 12OI (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 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

26 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

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