Option-Implied Volatility Measures and Stock Return Predictability

Transcription

1 Opion-Implied Volailiy Measures and Sock Reurn Predicabiliy Xi Fu * Y. Eser Arisoy Mark B. Shackleon Mehme Umulu Absrac Using firm-level opion and sock daa, we examine he predicive abiliy of opion-implied volailiy measures proposed by previous sudies and recommend he bes measure using upo-dae daa. Porfolio level analysis implies significan non-zero risk-adjused reurns on arbirage porfolios formed on he call-pu implied volailiy spread, implied volailiy skew, and realized-implied volailiy spread. Firm-level cross-secional regressions show ha, he implied volailiy skew has he mos significan predicive power over various invesmen horizons. The predicive power persiss before and afer he 2008 Global Financial Crisis. Key words: opion-implied volailiy; volailiy skew; reurn predicabiliy JEL classificaion: G11; G12 We would like o hank Sephen Figlewski (he Edior) for providing us wih exremely insighful commens and consrucive suggesions. We hank Ser-Huang Poon, Meeo Sandri, Sephen Taylor, and all paricipans a 2014 Paris Financial Managemen Conference, and he New Financial Realiy Seminar a he Universiy of Ken for helpful commens. * Corresponding auhor. Deparmen of Economics, Finance and Accouning, Universiy of Liverpool Managemen School, Universiy of Liverpool, Chaham Sree, Liverpool L69 7ZH, UK, Tel: +44(0) , Fax: +44(0) , Xi.Fu@liverpool.ac.uk. Universié Paris-Dauphine, PSL Research Universiy, DRM Finance, Paris, France, Tel: +33(0) , eser.arisoy@dauphine.fr. Deparmen of Accouning and Finance, Lancaser Universiy Managemen School, Lancaser LA1 4YX, UK, Tel: +44(0) , m.shackleon@lancaser.ac.uk. Deparmen of Inernaional Trade and Finance, Yasar Universiy, Bornova, 35100, Izmir, Turkey, Tel: +90(0) , mehme.umulu@yasar.edu.r.

2 1 Inroducion Opions are forward-looking insrumens and opion-implied measures conain valuable informaion regarding invesors expecaions abou he reurn process of he underlying asse. Opion-implied volailiy has received paricular aenion due o he ime-varying propery of volailiy which is a widely used parameer in asse pricing. I is well-documened ha implied volailiy exraced from opion prices provides good forecass of fuure volailiy. 1 In a similar vein, recen sudies examine he predicive abiliy of differen opion-implied volailiy measures in he cross-secion of sock reurns. However, despie growing lieraure, here is no clear undersanding of i) wheher differen opion-implied volailiy measures capure disinc informaion abou he volailiy curve, ii) which measures are imporan for invesors in predicing sock reurns, and iii) which measures would ouperform in predicing sock reurns in dynamically managed porfolios. By comparing he predicive abiliy of alernaive opionimplied volailiy measures proposed in he lieraure, in he conex of reurn predicabiliy, his sudy highlighs wheher he proposed opion-implied volailiy measures are fundamenally differen o each oher and wheher heir predicive abiliy differs by invesmen horizon. 2 The relaionship beween opion-implied volailiy and sock reurn predicabiliy is of recen ineres. 3 For example, An, Ang, Bali and Cakici (2014) focus on he implied volailiy 1 See Chrisensen and Prabhala (1998), Szakmary, Ors, Kim and Davidson (2003), Poon and Granger (2005), Kang, Kim and Yoon (2010), Taylor, Yadav and Zhang (2010), Yu, Lui and Wang (2010), and Muzzioli (2011) for sudies on he predicive abiliy of opion-implied volailiy on fuure volailiy. 2 The opion-implied volailiy measures used in his sudy are: he call-pu implied volailiy spread ( CPIV ), he implied volailiy skew ( IVSKEW ), he above-minus-below ( AMB ), he ou-minus-a of calls ( COMA ), he ou-minus-a of pus ( POMA ), and he realized-implied volailiy spread ( RVIV ). Deails abou hese measures can be found in Secion For example, Arisoy (2014) uses reurns on crash-neural ATM sraddles of he S&P 500 index as a proxy of he volailiy risk, and reurns on OTM pus of he S&P 500 index as a proxy of he jump risk, and find ha he sensiiviy of sock reurns o innovaions in aggregae volailiy and marke jump risk can explain he differences beween reurns on small and value socks and reurns on big and growh socks. Doran, Peerson and Tarran (2007) find supporive evidence ha here is predicive informaion conen wihin he volailiy skew for shorerm horizon. 1

3 of individual opions and documen he significan predicive power of implied volailiy in predicing individual sock reurns. More specifically, large increases in call (pu) implied volailiies are followed by increases (decreases) in one-monh ahead sock reurns. Bali and Hovakimian (2009) invesigae wheher realized and implied volailiies can explain he crosssecion of monhly sock reurns and documen ha here is a posiive relaionship beween he call-pu implied volailiy spread and one-monh ahead sock reurns. Cremers and Weinbaum (2010) focus on he predicive power of he call-pu implied volailiy spread and provide evidence ha his measure predics weekly reurns o a greaer exen for firms facing a more asymmeric informaional environmen. Meanwhile, moivaed by he empirically documened volailiy skew for equiy opions, several sudies examine he predicive power of informaion capured by opions wih differen moneyness levels. 4 For example, Xing, Zhang and Zhao (2010) examine he implied volailiy skew, which is he difference beween ou-of-he-money pu and a-he-money call implied volailiies, and find a significanly negaive coefficien on he implied volailiy skew in Fama- MacBeh cross-secional regressions. Balussen e al. (2012) include four differen implied volailiy measures in heir sudy: ou-of-money volailiy skew (i.e., implied volailiy skew in Xing, Zhang and Zhao, 2010), realized versus implied volailiy spread, a-he-money volailiy skew (i.e., he difference beween he a-he-money pu and call implied volailiies), and weekly changes of a-he-money volailiy skew. By analyzing weekly sock reurns, hey find negaive relaionships beween weekly reurns and four opion-implied measures. In addiion o wo common facors used in previous sudies (a-he-money call-pu implied volailiy spread and ou-of-money implied volailiy skew), Doran and Krieger (2010) consruc hree oher 4 The phenomenon ha he implied volailiy of equiy opions wih low srike prices (such as deep ou-of-hemoney pus or deep in-he-money calls) is higher han ha of equiy opions wih high srike prices (such as deep in-he-money pus or deep ou-of-he-money calls) is known as volailiy skew (Hull, 2012). The volailiy skew is widely observed for equiy opions (Bollen and Whaley, 2004; Baes, 2003; Gârleanu, Pedersen, and Poeshman, 2007; and Xing, Zhang and Zhao, 2010). 2

4 measures based on implied volailiy exraced from call and pu opions. These hree measures are above-minus-below, ou-minus-a of calls, and ou-minus-a of pus. 5 Resuls in heir sudy show ha differences beween a-he-money call and pu implied volailiies and hose beween ou-of-he-money and a-he-money pu implied volailiies boh capure informaion abou fuure equiy reurns. From hese sudies, i is no clear wheher separaely consruced opion-implied volailiy measures in he lieraure capure fundamenally differen informaion in predicing sock reurns. In he presence of oher volailiy measures, some of hese volailiy measures may be redundan in predicing sock reurns. Building on aforemenioned sudies, his paper compares he abiliy of he various opion-implied volailiy measures o predic one-week o hree-monh ahead reurns. Addressing he quesion of which opion-implied volailiy measure(s) ouperforms alernaives in predicing sock reurns and wheher heir predicive abiliy persiss over differen invesmen horizons is crucial, having implicaions for porfolio managers and marke paricipans. These groups can adjus heir rading sraegies and form porfolios based on opion-implied volailiy measure(s) ha has he sronges predicive power and hus earn excess reurns. To compare he predicive power of opion-implied volailiy measures, we firs form quinile porfolios sored wih respec o six opion-implied volailiy measures: he call-pu implied volailiy spread (CPIV ), he implied volailiy skew ( IVSKEW ), he above-minusbelow ( AMB ), he ou-minus-a of calls (COMA), he ou-minus-a of pus ( POMA), and he realized-implied volailiy spread ( RVIV ). Then, we consruc zero-cos arbirage porfolios by aking a long posiion in porfolios wih he highes implied volailiy measure and a shor posiion in porfolios wih he lowes implied volailiy measure. The arbirage 5 The above-minus-below is he difference beween he mean implied volailiy of in-he-money pus and ouof-he-money calls and he mean implied volailiy of in-he-money calls and ou-of-he-money pus. Ou-minusa of calls (pus) is he difference beween he mean implied volailiy of ou-of-he-money calls (pus) and he mean implied volailiy of a-he-money calls (pus). 3

5 porfolio will have significanly non-zero reurn if here is a saisically significan relaionship beween sock reurns and he corresponding opion-implied volailiy measure. However, porfolio level analysis migh suffer from he aggregaion effec due o omission of useful informaion in he cross-secion because i does no conrol for he effecs of oher opionimplied volailiy measures and firm-specific effecs simulaneously. Consequenly, we furher perform firm-level cross-secional regressions o assess he predicive power of all six inerlinked opion-implied volailiy measures. Our sudy conribues o he lieraure in several aspecs. Firs, his sudy compares he predicive abiliy of six differen implied volailiy measures. To he bes of our knowledge, his is he mos comprehensive sudy ha compares he predicive power of opion-implied volailiy measures. Secondly, our sudy ess he predicive power of differen opion-implied volailiy measures on sock reurns over various invesmen horizons. This helps invesors beer undersand he informaional conen capured by differen opion-implied volailiy measures. Finally, he sample period, from 1996 unil 2014, is longer han hose used in previous sudies. This enables us o analyze wheher he predicive power of opion-implied volailiy measures documened previously is sill significan in exended periods using recen daa in he US markes. The paper is organized as follows. Secion 2 discusses he daa and he mehodology. Secion 3 examines he relaionship beween expeced sock reurns and differen opionimplied volailiy measures hrough porfolio level analysis and firm-level cross-secional regressions. Secion 4 discusses poenial reasons for he predicive power of opion-implied volailiy measures hrough discussions on informed rading, skewness preference, consrains on shor-sale, and dela hedging. Secion 5 offers concluding remarks. 4

6 2 Daa and Mehodology 2.1 Daa Sources Our daa come from several differen sources. Financial saemen daa are downloaded from Compusa, monhly and daily sock reurn daa are from CRSP, and opion implied volailiy daa are from OpionMerics. The facors in Fama-French (1993) hree-facor model (i.e., MKT, SMB, and HML ) are obained from Kenneh French s online daa library. 6 To disinguish a-he-money opions, we follow he crieria in Bali and Hovakimian (2009). 7 Tha is, if he absolue value of he naural logarihm of he raio of he sock price o he exercise price is smaller han 0.1, an opion is denoed a-he-money. We denoe opions wih he naural logarihm of he raio of he sock price o he exercise price smaller han -0.1 as ou-of-he-money call (in-he-money pu) opions. Opions wih he naural logarihm of he raio of he sock price o he exercise price larger han 0.1 are denoed in-he-money call (ouof-he-money pu) opions. Then, we calculae he average implied volailiies for differen kinds of opions across all eligible opions a he end of each calendar monh. Our sample period sars from January 1996 and ends in December 2014 (i.e., 19 years) Opion-Implied Volailiy Measures For equiy opions, i is normal o observe he exisence of volailiy skew (i.e., he volailiy decreases as he srike price increases). As discussed in he previous secion, 6 Available a: hp://mba.uck.darmouh.edu/pages/faculy/ken.french/daa_library.hml. 7 Only sock daa for ordinary common shares (CRSP share codes 10 and 11) are reained. Furhermore, closedend funds, REITs (SIC codes and 6798) and hose companies whose shares were rading less han $5 are excluded. For opion daa, we focus on he las rading day of each calendar monh. We only reain sock opions wih days-o-mauriy greaer han 30 bu less han 91 days. Afer deleing opions wih zero open ineres or zero bes bid prices and hose wih missing implied volailiy, we furher exclude opions whose bid-ask spread exceeds 50% of he average of he bid and ask prices and opions which are raded for less han $ The firs observaion of he implied volailiy is available a he end of January, So he reurn observaion sars from February, The las observaion of monhly sock reurns is he reurn in December, Since his sudy uses hree-monh holding period reurn, he las observaion for hree-monh reurn should be he reurn during he period from Ocober, 2014 o December, 2014, whereas he las observaion for each volailiy measure is consruced a he end of Sepember So he sample consiss of 225 monhly observaions. The sample size is discussed in deail in secion

7 empirical sudies documen ha a differen par of he volailiy curve can capure relevan informaion abou fuure sock reurns (Bali and Hovakimian, 2009; Balussen e al., 2012; Cremers and Weinbaum, 2010; Xing, Zhang and Zhao, 2010; Doran and Krieger, 2010; ec.). In following subsecions, we discuss how differen opion-implied volailiy measures reflec invesors expecaions abou fuure marke condiions Call-Pu Implied Volailiy Spread Drawing upon he mehod documened in Bali and Hovakimian (2009), CPIV is consruced as follows: CPIV IV IV (1) ATM, call ATM, pu where CPIV is he call-pu implied volailiy spread, IV ATM, call is he average of implied volailiies exraced from all a-he-money call opions, and IV ATM, pu is he average of implied volailiies exraced from all a-he-money pu opions available on he las rading day in each calendar monh. If invesors expec decreases in underlying asse prices in he near fuure, hey will choose o buy pu opions and sell call opions. In his case, prices of pu opions will increase while prices of call opions will decrease, suggesing higher implied volailiies for pu opions and lower implied volailiies for call opions. A more negaive CPIV predics decreases in underlying asse prices (i.e., more negaive reurns) and vice versa. Thus, i is expeced ha fuure asse reurns should be posiively correlaed wih CPIV Implied Volailiy Skew To consruc IVSKEW proposed by Xing, Zhang and Zhao (2010), we calculae he difference beween he average of implied volailiies exraced from ou-of-he-money pu opions and he average of implied volailiies exraced from a-he-money call opions: IVSKEW IV IV (2) OTM, pu ATM, call 6

8 where IVSKEW is he implied volailiy skew, IV OTM, pu is he average of implied volailiies exraced from ou-of-he-money pu opions a he end of each calendar monh. If invesors expec ha here will be a downward movemen in underlying asse price, hey will choose o buy ou-of-he-money pu opions. An increase in he demand for ou-of-hemoney pu opions furher leads o increases in heir prices, and hus in heir implied volailiies. In his case, he spread beween ou-of-he-money pu implied volailiies and a-he-money call implied volailiies will become larger. IVSKEW reflecs invesor s concern abou fuure downward movemens in underlying asse prices. A higher IVSKEW indicaes a higher probabiliy of large negaive jumps in underlying asse prices. So, IVSKEW is expeced o be negaively relaed o fuure reurns on underlying asses Above-Minus-Below AMB represens he difference beween average implied volailiy of opions whose srike prices are above curren underlying price and average implied volailiy of opions whose srike prices are below curren underlying price. Following Doran and Krieger (2010), his sudy defines AMB as: where ITM, pu IVITM, pu IVOTM, call IVITM, call IVOTM, pu AMB (3) 2 IV, IV OTM, call, IV ITM, call, and IV OTM, pu are mean implied volailiies of all in-hemoney pu opions, all ou-of-he-money call opions, all in-he-money call opions, and all ouof-he-money pu opions, respecively. The variable AMB capures he difference beween he average implied volailiies of high-srike-price opions and he average implied volailiies of low-srike-price opions. Thus, AMB capures he volailiy curve asymmery by invesigaing boh of is ails. More (less) negaive values of AMB are indicaions of more rading of pessimisic (opimisic) invesors and hus lower (higher) fuure sock reurns are expeced. 7

9 2.2.4 Ou-Minus-A Doran and Krieger (2010) also inroduce wo oher measures, which capure he difference beween ou-of-he-money and a-he-money implied volailiies of call/pu opions. COMA IV IV (4) OTM, call ATM, call POMA IV IV (5) OTM, pu ATM, pu All measures in hese wo equaions have he same meanings as in he previous equaions (1) (3). In conras o AMB, COMA ( POMA) use only ou-of-he-money and a-he-money call (pu) opions o capure he volailiy curve asymmery. In he opion marke, i is observed ha ou-of-he-money and a-he-money call and pu opions are he mos liquid and heavily raded whereas in-he-money opions are no raded much (Baes, 2000). I is also repored ha bullish raders generally buy ou-of-he-money calls while bearish raders buy ou-of-he-money pus (Gemmill, 1996). To follow a rading sraegy based on volailiy curve asymmery, i is more convenien o consruc a measure using he mos liquid opions for which daa availabiliy is no a concern. Posiive COMA is associaed wih bullish expecaions, indicaing an increase in he rading of opimisic invesors. However, a posiive POMA reflecs he overpricing of ou-of-he-money pus relaive o a-he-money pus due o increased demand for ou-of-hemoney pus ha provide hedging agains negaive jump risk Realized-Implied Volailiy Spread In he spiri of Bali and Hovakimian (2009), we calculae realized volailiy ( RV ), which is he annualized sandard deviaion of daily reurns over he previous monh, and hen consruc a realized-implied volailiy spread, RVIV, as follows: where RVIV RV IV ATM (6) IV ATM is he average implied volailiy of a-he-money call and pu opions. 8

10 The variable RVIV is relaed o volailiy risk, which has been widely esed in empirical papers. When esing he volailiy risk premium, previous aricles focus on he difference beween realized volailiy and implied volailiy (proxied by a variance swap rae). However, raher han using a variance swap rae (which is calculaed by using opions wih differen moneyness levels), we focus on a-he-money implied volailiy (a sandard deviaion measure) Discussion on Opion-Implied Volailiy Measures To beer show ha various opion-implied volailiy measures capure differen informaion abou he volailiy curve, Exhibi 1 plos call and pu implied volailiies of Adobe Sysem Inc. on December 29, Opions included in his Exhibi have an expiraion dae of February 17, 2001 (i.e., wo monhs ahead). [Inser Exhibi 1 here] From his exhibi, i is clear ha CPIV capures he middle of he volailiy curve, which reflecs small deviaions from pu-call pariy. IVSKEW reflecs he lef of he pu volailiy curve and he middle of he call volailiy curve. The AMB measure capures he ails of he volailiy curve. COMA capures he righ side and middle of he volailiy curve for call opions, while POMA capures he lef side and middle of he volailiy curve for pu opions. From call and pu opions wih he same srike price and ime-o-expiraion, i is easy o observe small deviaions from pu-call pariy. Tha is, small differences beween paired call and pu implied volailiies are apparen. However, hese deviaions do no necessarily indicae arbirage opporuniies (discussed in Secion 4.5). Furhermore, measures IVSKEW, AMB, COMA and POMA provide some indicaions abou he shape of he implied volailiy curve. Lower AMB and COMA indicae more negaively skewed implied volailiy curves. Lower POMA and IVSKEW indicae less negaively skewed implied volailiy curves. 9 Thus, we 9 Compared o POMA, IVSKEW uses a-he-money call opions, which are more liquid han a-he-money pu opions and are seen as he invesors consensus on he firm s uncerainy (Xing, Zhang and Zhao, 2010). 9

11 expec o observe a posiive relaionship beween AMB or COMA and sock reurns, bu a negaive relaionship beween IVSKEW or POMA and sock reurns. Overall, CPIV, IVSKEW, AMB, COMA and POMA capure differen pars of he volailiy curve. Therefore i is ineresing o es wheher hese measures (i.e., differen pars of he volailiy curve) have differen predicive abiliy for asse reurns. Taken ogeher, all five opion-implied volailiy measures capure much of he informaion conained in he crosssecion of implied volailiies (Doran and Krieger, 2010). However, some of hem are inerdependen, e.g., IVSKEW POMA CPIV. So, hese hree measures canno be included in he same model because of he muli-collineariy problem. In addiion o hese measures, we furher include anoher volailiy measure used in Bali and Hovakimian (2009), RVIV. 2.3 Firm Specific Variables In order o see wheher opion-implied volailiy measures can predic sock reurns afer conrolling for known firm-specific effecs, we also include several firm-level conrol variables. To conrol for he size effec documened by Banz (1981), we use he naural logarihm of a company s marke capializaion (in housands of USD) on he las rading day of each monh. Following Fama and French (1992), we use he book-o-marke raio as anoher firm-level conrol variable. Jegadeesh and Timan (1993) documen he exisence of a momenum effec (i.e., pas winners, on average, ouperform pas losers in shor fuure periods). We use pas onemonh reurns o capure he momenum effec. Sock rading volumes are included as anoher variable (measured in hundred millions of shares raded in he previous monh). The marke bea reflecs he hisorical sysemaic risk and is calculaed by using daily reurns available in he previous monh using he sandard CAPM framework. 10 The bid-ask spread is used o conrol for liquidiy risk. I is defined as he mean daily percenage bid-ask spread over he previous monh where he percenage bid-ask spread is he difference beween ask and bid 10 I is required ha socks should have more han 15 daily observaions in he previous monh for bea calculaion. 10

12 prices scaled by he mean of he bid and ask prices (Bali and Hovakimian, 2009). Finally, we also conrol for opion rading volume (measured in millions of opions raded in he previous monh), which is documened o conain informaion abou fuure sock prices Resuls 3.1 Descripive Resuls Exhibi 2 presens some descripive saisics, such as mean, sandard deviaion, minimum, 5 h percenile, 25 h percenile, median, 75 h percenile, 95 h percenile and maximum of each volailiy measure, sample size available for each measure, as well as pairwise correlaions. 12 [Inser Exhibi 2 here] On he basis of all available observaions on he las rading day of each monh during he sample period, Panel A of Exhibi 2 repors descripive saisics for opion-implied volailiy measures. Therefore, he sample size varies for each measure. I is observed ha CPIV, AMB, COMA and RVIV have negaive means, while hose for IVSKEW and POMA are posiive. The las column of Panel A shows ha, he sample size for CPIV is larges (i.e., 230,884), whereas he sample size for AMB is smalles (i.e., 66,104). CPIV is consruced by using near-he-money call and pu opions while AMB is consruced by using deep ou-of-hemoney and in-he-money call and pu opions. I is expeced ha more near-he-money opions are available han deep ou-of-he-money and in-he-money opions. So he larger sample size for CPIV and he much smaller sample size for AMB are reasonable. Panel B of Exhibi 2 repors he descripive saisics of he inersecion sample which consiss of socks wih all opion-implied volailiy measures available. The inersecion sample 11 Pan and Poeshman (2006) find srong evidence ha opion rading volume conains informaion abou fuure sock prices. Doran, Pererson, and Tarran (2007) incorporae opion rading volume when analyzing wheher he shape of implied volailiy skew can predic he probabiliy of a marke crash or spike. 12 The opion-implied volailiy measures in Exhibi 2 are repored in decimals, no in percenages. The full sample presened in Panel A consiss of 4,999 US firms, and he inersecion sample in Panel B consiss of 3,317 US firms. 11

13 has 62,562 sock-monh observaions. 13 CPIV, AMB, COMA and RVIV have negaive means, whereas IVSKEW and POMA have posiive means. The negaive sample mean of CPIV shows ha pu opions on individual companies end o have higher average implied volailiy han calls. Individual firms end o have negaive implied volailiy skew as seen by he posiive sample means of POMA and IVSKEW and negaive sample means of AMB and COMA. These resuls suppor he view ha, on average, implied volailiy curve is asymmeric for individual equiies as observed in Exhibi 1. As discussed in Secion 2.2, IVSKEW is he difference beween POMA and CPIV. On average, percen of he value of he negaive skew sems from he difference beween ahe-money implied volailiy of pus and a-he-money implied volailiy of calls, and he oher percen can be due o he difference beween ou-of-he-money implied volailiy and ahe-money implied volailiy of pus. Given he posiive relaionship beween sock reurns and CPIV and he negaive relaionship beween socks reurns and IVSKEW documened in previous sudies (Bali and Hovakimian, 2009; Cremers and Weinbaum, 2010; Doran and Krieger, 2010; and Xing, Zhang and Zhao, 2010), we infer wheher or no POMA (which represens he lef-hand side of he pu implied volailiy curve) plays a significan role in predicing sock reurns. If here is no empirical evidence in favor of significan predicive abiliy for POMA, he predicive power of IVSKEW should be driven by he difference beween a-he-money pu implied volailiies and he a-he-money call implied volailiies. Panel C of Exhibi 2 presens pairwise correlaions; here are four high average correlaions. The correlaion beween CPIV and IVSKEW is , he correlaion beween IVSKEW and POMA is , he correlaion beween AMB and COMA is 13 The inersecion sample in Doran and Krieger (2010) consiss of 62,076 company monhs during he period from January 1996 o Sepember Thus, he size of our inersecion sample during he same period is smaller han ha of Doran and Krieger (2010). This can be due o he differen moneyness crieria and more conrol variables used in his sudy. 12

14 0.6678, and he correlaion beween AMB and POMA is Oher pairwise correlaions are relaively low. These high correlaions indicae ha here migh be some informaion overlap in opion-implied measures. By rying o avoid overlap, his sudy akes ino accoun poenial mulicollineariy problem when conducing mulivariae firm-level cross-secional regressions. 3.2 Porfolio Level Analysis In order o examine he relaionship beween quinile porfolio reurns and each volailiy measure, we consruc quinile porfolios, and furher form a 5-1 arbirage porfolio wihin he full sample by holding a long posiion on he quinile porfolio wih he highes volailiy measure and a shor posiion on he quinile porfolio wih he lowes volailiy measure. Then, we es he null hypohesis ha he 5-1 arbirage porfolio has a mean reurn equal o zero. If he average reurn on he 5-1 arbirage porfolio is significanly posiive (negaive), here is a posiive (negaive) relaionship beween he volailiy measure and porfolio reurns. Resuls for porfolio level analysis are presened in Exhibi 3. [Inser Exhibi 3 here] We firs examine he effec of CPIV on subsequen one-monh porfolio reurns. For boh equally-weighed and value-weighed porfolios, reurns increase monoonically from porfolios wih he lowes CPIV o porfolios wih he highes CPIV. The mean reurn on he equally-weighed 5-1 arbirage porfolio is 1.12% per monh (wih a p-value close o 0), and he mean reurn on he value-weighed 5-1 arbirage porfolio is 0.97% per monh (wih a p- value of ). Significan posiive mean reurns on 5-1 arbirage porfolios indicae a posiive relaionship beween CPIV and porfolio reurns. We also conrol for Fama-French risk facors o examine wheher here are risk-adjused reurn differences for arbirage porfolios. Resuls are consisen wih hose obained for raw reurn differences. Jensen s alpha wih respec o Fama-French hree-facor model is 1.16% per monh (wih a p-value close o 0) 13

15 for equally-weighed 5-1 arbirage porfolios and i is 1.10% per monh (wih a p-value of ) for value-weighed 5-1 arbirage porfolios. These resuls for CPIV are comparable wih he resuls in Bali and Hovakimian (2009). Bali and Hovakimian (2009) documen ha he equally-weighed (value-weighed) raw reurn on he arbirage porfolio is, on average, 1.425% (1.045%) per monh wih a -saisic of 7.9 (4.2) and he equally-weighed (valueweighed) Jensen s alpha on he arbirage porfolio is 1.486% (1.140%) wih a -saisic of 8.6 (4.5). Nex, we focus on he effec of IVSKEW. The resuls in Exhibi 3 show a monoonic decreasing paern in equally- and value-weighed porfolio reurns. Porfolios wih lower IVSKEW ouperform hose wih higher IVSKEW. Average monhly reurns on 5-1 equallyweighed and value-weighed arbirage porfolios are always negaive and saisically significan a a 5% level (-0.86% wih a p-value close o 0 and -0.64% wih a p-value of , respecively). The negaive relaionship beween IVSKEW and porfolio reurn is sill significan afer conrolling for marke excess reurns ( MKT ), size ( SMB ) and book-o-marke raio ( HML ). Exhibi 3 shows weak evidence for a negaive relaionship beween AMB and porfolio reurns. For equally-weighed 5-1 arbirage porfolio, Jensen s alpha wih respec o Fama- French hree-facor model is -0.44% per monh, which is marginally significan a a 10% level. Exhibi 3 also presens quinile porfolio level analysis resuls for wo ou-minus-a measures. For boh COMA and POMA, here is no evidence of a relaionship beween hese wo measures and one-monh ahead asse reurns (he average monhly reurn and Jensen s alpha wih respec o Fama-French hree-facor models on each 5-1 arbirage porfolio are no significanly non-zero). Finally, resuls in Exhibi 3 confirm a negaive relaionship beween RVIV and onemonh ahead porfolio reurns. Boh he average reurn and he Jensen s alpha decrease 14

16 monoonically from he porfolio wih he lowes RVIV o ha wih he highes RVIV. Such a negaive relaionship is always significan a a 5% level no maer wheher he reurn is riskadjused or no. For example, Jensen s alpha for an equally-weighed 5-1 arbirage porfolio is -0.57% per monh wih a p-value of and ha for value-weighed 5-1 arbirage porfolio is -0.64% per monh wih a p-value of These resuls are broadly comparable o resuls in Bali and Hovakimian (2009). They documen ha Jensen s alpha for he arbirage porfolio consruced on RVIV is % wih a significan -saisic of -2.5 when using he equally-weighed scheme, and % wih a significan -saisic of -2.2 when using he value-weighed scheme. To summarize, resuls in Exhibi 3 confirm ha CPIV is posiively relaed o one-monh ahead porfolio reurns, whereas IVSKEW and RVIV are negaively relaed. Exhibi 3 also provides weak evidence abou he negaive relaionship beween AMB and porfolio reurns. However, hrough porfolio level analysis, COMA and POMA do no have significan power o explain one-monh ahead porfolio reurns. Alhough porfolio level analysis helps deermine poenial candidaes among several opion-implied volailiy measures in predicing fuure reurns, i does no allow us o conrol for firm-specific effecs. Some oher firm-specific effecs may also play a role in explaining sock reurns. To address his issue, we perform firm-level cross-secional regressions in he following subsecion. 3.3 Firm-Level Cross-Secional Regression Resuls This subsecion provides resuls from firm-level cross-secional regressions wih firmspecific conrol variables (i.e., size, book-o-marke raio, previous one-monh reurn, sock rading volume, hisorical bea, bid-ask spread, and opion rading volume). In he firs sep of firm-level cross-secional regressions, a he end of each calendar monh, sock reurns of differen firms are regressed on explanaory variables (e.g., opion-implied volailiy measures 15

17 and conrol variables) cross-secionally. Thus, during he full sample period, here are 225 esimaions for he coefficien on each explanaory variable. In he second sep, we es wheher he coefficien on each explanaory variable has non-zero ime-series mean. Firs, crosssecional regressions focus on he predicive power of each of several opion-implied volailiy measures, CPIV, IVSKEW, AMB, COMA, POMA and RVIV. Then, various volailiy measures are included in he same model in order o compare he predicive power of each measure. Such an analysis sheds ligh on which volailiy measure is he mos useful in predicing individual sock reurns. Furhermore, we es he predicive abiliy of differen opion-implied volailiy measures over various invesmen horizons from one week o hree monhs. Resuls for one-week and wo-week horizons and resuls for wo-monh and hree-monh horizons are similar. Therefore, we only repor he resuls for one-week, one-monh and hree-monh invesmen horizons o save space. 14 Finally, we perform subperiod analysis and compare resuls before and afer he 2008 Global Financial Crisis The Full Period Analysis Firs, we examine he predicive power of each volailiy measure covering he full sample period. Then, we es how each volailiy measure performs when compeing wih ohers hrough mulivariae regressions. Exhibi 4 shows resuls for he one-week invesmen horizon. [Inser Exhibi 4 here] Models I o VI focus on he predicive power of each opion-implied volailiy measure individually. Model I indicaes ha socks wih higher CPIV ouperform hose wih lower CPIV in he following one-week period. Such a posiive relaionship beween CPIV and sock reurns is significan a a 1% level. Model II invesigaes how IVSKEW correlaes wih one-week ahead sock reurns. The saisically significan and negaive coefficien on 14 Resuls for wo-week and wo-monh invesmen horizons are available upon reques. 16

18 IVSKEW confirms a negaive relaionship beween sock reurns and IVSKEW. Model III provides evidence in favor of a marginally significan predicive abiliy of AMB. Inconsisen wih our expecaions, empirical resuls show ha AMB is negaively relaed o one-week ahead sock reurns. For he one-week invesmen horizon, we do no find any evidence abou he significan impac of COMA, POMA or RVIV on ock reurns. The remaining four models in Exhibi 4 (Models VII o X) invesigae which opionimplied volailiy measures have sronger predicive power when compeing wih oher measures. Models VIII and X indicae ha among six opion-implied volailiy measures, IVSKEW has significan predicive power. 15 Furhermore, Models VII and IX indicae ha boh CPIV and POMA play imporan roles in explaining he significan predicive power of IVSKEW. Tha is, boh a-he-money call and pu opions and ou-of-he-money pu opions capure relevan informaion abou reurn predicion. The mulicollineariy issue may affec he significan coefficien on AMB. In hese hree models, he relaionship beween AMB and one-week ahead sock reurns becomes sronger compared o wha is shown in Model III of Exhibi 4. As discussed in subsecions and 2.2.6, AMB measures he volailiy curve asymmeries. Compared wih hree oher measures ( IVSKEW, COMA and POMA) ha reflec he shape of implied volailiy curve, AMB is consruced using boh in-he-money and ou-of-he-money opions. In-he-money opions may no capure informaion as we expec due o infrequen rading aciviy. Finally, over he one-week horizon, RVIV has marginally significan power in predicing fuure sock reurns when compeing wih oher opion-implied volailiy measures. This is consisen wih he finding of porfolio level analysis discussed in Secion If IVSKEW and CPIV / POMA are included in he same muli-variae regression model, IVSKEW sill gains significan predicive abiliy whereas he predicive power of CPIV / POMA disappears. 17

19 In order o examine wheher he predicive power of differen opion-implied volailiy measures persiss over longer periods, we invesigae how differen measures perform in predicing one-monh ahead sock reurns. Exhibi 5 presens corresponding resuls. [Inser Exhibi 5 here] Models I and II indicae ha he predicive power of CPIV or IVSKEW persiss over a longer invesmen horizon. Model V of Exhibi 5 indicaes ha a higher POMA predics lower one-monh ahead sock reurn. Such a negaive relaionship is significan a a 5% level. Then, Models VIII o X indicae ha, when compeing wih oher opion-implied volailiy measures, IVSKEW has addiional significan predicive power. The significan and negaive slope on IVSKEW is driven by deviaions from pu-call pariy and volailiy curve asymmery. As shown in Models VII and IX, even hough boh CPIV and POMA have significan slopes, he predicive power of CPIV is more significan. Compared o resuls in Exhibi 4, RVIV loses i predicive power for he one-monh horizon. Finally, we es he predicabiliy of differen opion-implied volailiy measures over he hree-monh horizon. [Inser Exhibi 6 here] As shown in Exhibi 6, regression models focusing on each individual opion-implied volailiy measure (Models I o VI) furher confirm he predicive power of CPIV, IVSKEW, and POMA on sock reurns. In he remaining four models (Models VII o X), i is obvious ha he predicabiliy of IVSKEW sems from informaion capured by boh CPIV and POMA. Meanwhile, ou-of-he-money call implied skew becomes imporan in reurn predicion, since COMA has a marginally significan and posiive slope in cross-secional regressions (Models VII and IX). Resuls in Exhibis 4 o 6 imply an asymmeric effec of he volailiy risk. As can be inferred from Exhibi 1, COMA reflecs informaion on he righ and middle par of he 18

20 volailiy curve, and IVSKEW and POMA reflec informaion on he lef and middle par of he volailiy curve. The righ par of he implied volailiy curve capures posiive informaion (invesors wih bullish expecaions choose o rade ou-of-he-money call opions), while he lef par of he implied volailiy curve acually capures negaive informaion (invesors choose o rade ou-of-he-money pu opions o be proeced from large negaive jumps). Resuls for mulivariae regressions reflec ha invesors may rea hese wo kinds of informaion differenly. For shorer invesmen horizons, invesors are more sensiive o negaive informaion capured by ou-of-he-money pu opions, and such a kind of informaion predics fuure sock reurns. For longer horizons, here is more uncerainy abou fuure marke condiions, and here is a higher chance ha ou-of-he-money call opions come in-he-money a mauriy. Informaion capured by ou-of-he-money call opions becomes increasingly imporan as invesmen horizons exend. Thus, COMA predics sock reurns over longer horizons. Even hough boh COMA and POMA capure he shape of he implied volailiy curve, hese wo measures do no predic sock reurns in he same way. From resuls discussed in his subsecion, i is inferred ha, among all six opion-implied volailiy measures, IVSKEW has he mos significan power in predicing fuure sock reurns. 16 For he one-week invesmen horizon, he significan effec of IVSKEW is affeced by deviaions from pu-call pariy and he lef par of implied volailiy curve. For one-monh and hree-monh horizons, he predicive power of POMA becomes weaker. For longer invesmen horizons, like hree-monh, posiive news is imporan for invesors since hey are more opimisic abou he long-erm performance of he marke. Thus, COMA gains a significan coefficien in cross-secional regressions. 16 In addiion o firm-level cross-secional regressions, his sudy also performs pooled regressions for he sample, which involves boh ime-series and cross-secional daa. Resuls for pooled regressions confirm he imporance of CPIV and IVSKEW in predicing fuure sock reurns over various horizons from one-week o hree-monh. A higher CPIV predics a higher fuure sock reurn, whereas a higher IVSKEW predics a lower fuure sock reurn. Furhermore, conrolling for ime fixed effecs does no affec he significance of he predicive power of CPIV and IVSKEW. More deailed resuls are available upon requess. 19

21 3.3.2 The Subperiod Analysis Our sample period is from 1996 o 2014, and i covers he 2008 Global Financial Crisis. I is ineresing o examine wheher informaion capured by differen kinds of opions is perceived in he same way before and afer he recen financial crisis. In his subsecion, firmlevel cross-secional regressions are conduced for wo subperiods: before and afer Sepember Exhibis 7 and 8 show how opion-implied volailiy measures perform in predicing oneweek ahead sock reurns before and afer he crisis, respecively. [Inser Exhibis 7 & 8 here] Compared o resuls presened in Exhibi 4, similar resuls can be found in Exhibis 7 and 8. Tha is, IVSKEW is imporan in predicing one-week ahead sock reurns in boh subperiods. The role played by CPIV or POMA seems o change during wo subperiods. CPIV has predicive power before he crisis, bu is predicive abiliy does no persis afer he crisis. However, for POMA, he predicabiliy over he one-week horizon becomes sronger afer he crisis. Afer he crisis, invesors would be more sensiive o negaive shocks (i.e., crashes) capured by he lef par of he pu implied volailiy curve. Thus, for he one-week invesmen horizon, poenial negaive jumps capured by IVSKEW would conain relevan informaion abou sock reurn predicion. No maer which sample period is invesigaed, he predicabiliy of IVSKEW a he one-week horizon is sronger han any oher measures used in his sudy. 4. Discussion Resuls of empirical ess presened above provide useful insighs abou how opionimplied volailiy measures perform in predicing fuure sock reurns. From Exhibi 1, i is clear ha differen opion-implied volailiy measures capure differen porions of he implied volailiy curve. Thus, differen volailiy measures perform differenly in predicing sock 20

22 reurns. This secion discusses why some measures (especially IVSKEW and CPIV ) dominae ohers in predicing fuure sock reurns. 4.1 Informed Trading The volailiy curve asymmery could be due o invesors rading in opion markes (Bollen and Whaley, 2004). When he demand for a paricular opion conrac is srong, due o arbirage limis, compeiive risk-averse opion marke makers are no able o hedge heir posiions perfecly and hey require a premium for aking his risk. As a resul, he demand for an opion drives up is price. In his ype of equilibrium, one would expec a posiive relaion beween opion expensiveness which can be measured by implied volailiy and end-user demand. Invesors wih posiive (negaive) expecaions abou he fuure marke condiions will increase heir demand for call (pu) opions and/or reduce heir demand for pus (calls), implying an increase in call (pu) implied volailiy and/or a decrease in pu (call) implied volailiy. By using a VAR-bivariae-GARCH model, Bali and Hovakimian (2009) provide evidence supporing a significan volailiy spillover effec where informaion propagaes from individual equiy opions o individual socks. Due o his spillover effec, opion-implied informaion could conain useful informaion abou sock reurn predicion. From he previous lieraure, if invesors choose o rade in opion markes firs, heir rading aciviies will generae volailiy curve asymmery. The volailiy curve asymmery capures relevan informaion in predicing fuure sock reurns due o spillover effec from opion markes o sock markes. Previous lieraure discusses poenial reasons which drive rading aciviies in opion markes. Bali and Hovakimian (2009) claim ha informed invesors, who know ha sock prices will change bu are no sure abou he direcion, choose o rade in opion markes. This could be due o he fac ha opions provide leverage for invesors; invesors ge much higher 21

23 profis from rading opions han hose from rading underlying socks. Also, rading opions provide insurance for undesirable changes in underlying asse prices. Cremers and Weinbaum (2010) show ha deviaions from pu-call pariy are more likely o occur in socks wih high probabiliy of informed rading (PIN), supporing he view ha CPIV conains informaion abou fuure prices of underlying socks. Furhermore, deviaions from pu-call pariy end o predic reurns o a greaer exen in firms ha face a more asymmeric informaion environmen. Consisenly, Xing, Zhang and Zhao (2010) find ha he predicive power of he implied volailiy skew is driven by informed rading. Tha is, informed raders ac in he opions marke and ha he sock marke is slow o incorporae informaion from he opions marke. Furhermore, informaion capured by he implied volailiy skew is closely relaed o firm fundamenals, which can predic subsequen underlying asse reurns. Lin and Lu (2015) documen ha insider raders choose o rade in opion markes firs. The predicive power of opion implied volailiies on sock reurns becomes sronger around analys-relaed evens. This finding suppors he argumen ha he predicabiliy of opionimplied volailiies is driven by insiders informaion on upcoming analys-relaed news. Overall, opion-implied informaion capures relevan informaion abou fuure movemens in underlying asse prices due o he spillover effec of informed rading from opion markes o sock markes. 4.2 Skewness Preference Invesors preference over skewness also helps explain he relaionship beween opionimplied volailiy measures and fuure sock reurns. Bakshi, Kapadia and Madan (2003) show ha a more negaive risk-neural skewness is equivalen o a seeper slope of implied volailiy curve, everyhing else being equal. This indicaes a negaive relaionship beween IVSKEW / POMA and risk-neural skewness and a posiive relaionship beween AMB /COMA and risk 22

24 neural skewness. The negaive relaionship beween IVSKEW ( POMA ) and fuure sock reurns shown in previous analysis indicaes a negaive skewness preference. However, he negaive relaionship beween AMB and fuure sock reurns shows conflicing findings: a posiive skewness preference. Exising lieraure also documens mixed resuls abou skewness preference. Bali, Cakici and Whielaw (2011), Bali and Murray (2013), and Conrad, Dimar and Ghysels (2013) find a posiive skewness preference, whereas Rehman and Vilkov (2012), Silger, Kosakis and Poon (2016), and Xing, Zhang and Zhao (2010) documen a negaive skewness preference. Due o mixed findings abou skewness preference in previous lieraure, Lazos, Coakley and Liu (2015) invesigae how heerogeneous expecaions affec skewness preference. Their empirical analysis shows ha when invesors are pessimisic (opimisic), heir overconfidence produces an undervaluaion (overvaluaion) which explains heir negaive skewness preference. The overconfidence of neural invesors who exhibi eiher pessimism or opimism leads o overvaluaion of asses, indicaing a posiive skewness preference. Thus, invesors wih heerogeneous expecaions may have differen preference over skewness. Variables IVSKEW and POMA capure pessimisic fears. The negaive relaionship beween IVSKEW / POMA and sock reurns are consisen wih he negaive skewness preference of pessimisic invesors. The variable AMB capures neural expecaions (pessimisic expecaions in he lef ail and opimisic expecaions in he righ ail). Due o he posiive relaionship beween AMB and risk neural skewness, a negaive relaionship beween AMB and sock reurns indicaes ha invesors are willing o accep lower reurns in order o pursue higher skewness. This is consisen wih he posiive skewness preference of neural invesors. 23

25 4.3 Pu-Call Pariy Nex, we focus on why call-pu implied volailiy spreads (capuring deviaion from pucall pariy) predic fuure sock reurns. Pu-call pariy indicaes a relaionship beween prices of call and pu opions wih he same expiraion dae and srike price. P S D C Ke r( T ) (7) where is he curren ime, T is he ime of expiraion, S is he price of he underlying asse, K is he srike price, r is he coninuous risk-free rae, paid on he underlying asse before expiraion, and D is he presen value of dividends C and P are prices of call and pu opions. I is expeced ha equaion (7) holds in perfec markes. Due o he exisence of marke fricions, following Finucane (1991), he pu-call pariy afer conrolling opion bid-ask spread could be wrien as: P C Ke S D 0 (8) a b r( T ) where b P, b C, a P and bid-ask spreads of he call and pu opions, a b C P K S D 0 (9) a C are he pu and call bid and ask prices. Defining C and P as he C C (10) a b C P P (11) b a P and subsiuing (10) and (11) ino (9) yields he second condiion in erms of Defining b C and a P : b a C P C P K S D ( ) 0 (12) E C P Ke S D (13) b a r ( T ) and subsiuing ino (8) and (12) yields he fricionless marke bounds for he measure E K e r( T ) C P ( 1) E 0 (14) 24

26 E, which may be inerpreed as a measure of deviaion from pu-call pariy, is used as he basic measure of relaive pu and call prices. Higher values of high relaive o pus, and lower values imply relaively high pu prices. By calculaing E mean ha calls are priced E for each individual asse, we are able o disinguish socks wih no violaion of equaion (14) and we would expec ha pu-call pariy holds by definiion for hese socks. For hese socks, we es wheher CPIV capures imporan informaion abou fuure sock reurns. For socks wih no deviaion from pu-call pariy under he conrol of opion bidask spread from equaion (14), resuls show ha CPIV is sill significanly and posiively relaed o fuure sock reurns. 17 The upper and lower bounds used in equaion (14) fail o reflec oher fricions, such as consrains on shor sale. Tha is, for socks wih no deviaion from pu-call pariy afer conrolling for opion bid-ask spread, CPIV sill has significan predicive power. This may indicae ha he marke is no fricionless and opion-implied volailiy measures capure oher relevan informaion, such as consrains on shor sale, which are discussed in he nex subsecion. 4.4 Shor Sale Consrains In sock markes, following a buy-and-hold sraegy generaes profis if sock price increases. On he oher hand, o avoid poenial loss due o a decrease in a sock price in he fuure, pessimisic invesors holding he sock choose o sell i. Pessimisic invesors who do no hold he sock are able o make profis only by shor selling he sock. In order o shor sell a sock, borrowers have o find lenders who hold he sock and are willing o lend he sock o ohers. Afer posing a collaeral as required, borrowers can borrow 17 The resuls for porfolio level analysis on CPIV among socks wih no deviaion from pu-call pariy as shown in equaion (14) show ha he average reurn on he equally-weighed 5-1 long-shor porfolio consruced on CPIV is 0.88% per monh (wih a p-value close o 0), and he average reurn on he value-weighed 5-1 longshor porfolio is 0.71% per monh (wih a p-value of ). More deails are available upon reques. 25