THE IMPLIED VOLATILITY OF ETF AND INDEX OPTIONS

The Internatonal Journal of Busness and Fnance Research Volume 5 Number 4 2011 THE IMPLIED VOLATILITY OF ETF AND INDEX OPTIONS Stoyu I. Ivanov, San Jose State Unversty Jeff Whtworth, Unversty of Houston-Clear Lake Y Zhang, Prare Vew A&M Unversty ABSTRACT We examne the opton-mpled volatlty of the three most lqud ETFs (Damonds, Spders, and Cubes) and ther respectve trackng ndces (Dow 30, S&P 500, and NASDAQ 100). We fnd that volatlty smles for ETF optons are more pronounced than for ndex optons, prmarly because deep-n-themoney ETF optons have consderably hgher mpled volatlty than deep-n-the-money ndex optons. The observed dfference n mpled volatlty s not due to a dfference between the realzed return dstrbutons of the underlyng ETFs and ndces. Dfferences n mpled volatlty for ETF and ndex optons also do not appear to be explaned by dscrepances n net buyng pressure, as theorzed by Bollen and Whaley (2004). JEL: G11; G12 KEYWORDS: exchange-traded funds, ndex optons, mpled volatlty, open nterest INTRODUCTION I n ths paper, we study the opton-mpled volatlty of exchange-traded funds (ETFs) and ther trackng ndces. ETFs are relatvely cheap nstruments for dversfcaton n terms of drect costs. They have greatly ncreased n popularty and have become mportant nvestment vehcles for both professonal and ndvdual nvestors. The Investment Company Insttute (ICI) reports that there were 80 ETFs n 2000 and 359 ETFs n 2006, a 350 percent ncrease. ETF assets also ncreased sgnfcantly from $65.59 bllon n 2000 to $422.55 bllon n 2006, an ncrease of 544 percent for the perod. Most of the lterature on ETFs focuses on ther trackng errors relatve to ther respectve ndces. However, very lttle research has been conducted on ETF volatlty. The paper contrbutes to the lterature n several ways. Frst, the paper flls the vod n the exstng lterature on the volatlty of ETFs, whch play an mportant role n rsk dversfcaton. We examne both the realzed return volatlty and the opton-mpled volatlty a commonly used estmate of future volatlty. We fnd that the mpled volatlty of ETF optons s dfferent from that of ndex optons, especally for deep-n-the-money optons. However, we fnd no sgnfcant dfference n the realzed return volatltes of ETFs versus ther ndces. Second, the paper adopts a unque sample to reexamne the net buyng pressure theory of Bollen and Whaley (2004). The advantage of usng par samples of ETF optons and ndex optons s that return dstrbutons of ETFs are nsgnfcantly dfferent from those of ther trackng ndces. Our results are nconsstent wth the argument of Bollen and Whaley (2004) that an opton s mpled volatlty functon should be postvely related to ts net buyng pressure. Therefore, the dfference n mpled volatlty functons between ETFs and ndces can be attrbuted to other factors. The remander of ths paper s organzed as follows: The next secton examnes the related lterature and develops the scope of ths research study. We then descrbe our data and methodology and dscuss the results of our emprcal tests. The fnal secton concludes. 35

S. I. Ivanov et al IJBFR Vol. 5 No. 4 2011 LITERATURE REVIEW AND RESEARCH DEVELOPMENT In recent years, ETFs have exploded n popularty as nvestment tools. However, most of the extant lterature on ETFs focuses on ther trackng error (e.g., Poterba and Shoven, 2002; Engle and Sarkar, 2006). To our knowledge there are no studes on the volatlty of ETFs. In a study of the excess volatlty characterstcs of closed-end funds, Pontff (1997) fnds that closed-end funds are more volatle than ther underlyng securtes. Closed-end funds are smlar to ETFs n that both are traded on a stock exchange throughout the tradng day, but ETFs are structured dfferently from closed-end funds. For example, ETFs legally resemble open end funds n the sense that new ETF securtes can be ssued. ETFs are passve nvestment vehcles. The ETF manager closely tracks the yeld and prce of the underlyng ndex by acqurng the stocks n the ndex. Nevertheless, ETFs do not necessarly mmc ther underlyng ndces perfectly for several reasons. Frst, the proportons and exact composton of the ETF portfolo mght dffer slghtly from that of the underlyng ndex as the portfolo manager seeks to mnmze costs. Second, ETFs accumulate dvdends n a non-nterest bearng account and dstrbute accumulated dvdends n a lump sum perodcally. (Spders and Cubes dstrbute dvdends quarterly, whle Damonds pay dvdends monthly.) Thrd, ETFs contnue tradng after hours untl 4:15 p.m., whle ndces are reported at 4:00 p.m. These dfferences may cause the return of an ETF to devate from that of ts underlyng ndex. Chrstensen and Prabhala (1998) show that a stock s future volatlty s predcted more relably by the opton-mpled volatlty than by the stock s past realzed volatlty. Therefore, we also nvestgate the mpled volatlty of the three best-known and most lqud ETFs: Damonds, Spders, and Cubes. These ETFs track the yeld and prce of the Dow Jones Industral Average (.e., Dow 30), S&P 500, and NASDAQ 100, respectvely. ETFs are traded lke stocks, so ETF optons can be consdered stock optons. The exstng lterature shows that the mpled volatlty functon of stock optons s dfferent from that of ndex optons. Baksh, Kapada, and Madan (2003) study S&P 100 ndex optons and the 30 largest stocks n the ndex and fnd that the ndex volatlty smle (the varaton of the mpled volatlty across strke prces) s more negatvely sloped than ndvdual stock volatlty smles. They show that ths dfference comes from the more skewed return dstrbuton of ndvdual stocks. Hence, we frst test whether the mpled volatlty functons of ETF and ndex optons dffer. We fnd that ETF optons commonly have hgher mpled volatltes than ther ndces, especally for deep-n-the-money optons. In vew of ths result, we examne not only the mean return of ETFs versus ther trackng ndces, but also the entre return dstrbuton. We focus on the hgher moments of return volatlty, skewness, and kurtoss. Usng realzed daly returns over a perod spannng more than sx years, we fnd no sgnfcant dfference between the return dstrbutons of ETFs and ndces. Snce ETFs track ther underlyng ndces closely and are not sgnfcantly dfferent from ther underlyng ndex n the return dstrbutons, ths produces a unque sample to explore the mpled volatlty of stock optons versus ndex optons. Bollen and Whaley (2004) argue that opton prces and mpled volatltes are affected by the demand for optons. When arbtrage s lmted, the opton supply curve s upward slopng so that mpled volatlty s related to the net buyng pressure from orders submtted by nvestors. Bollen and Whaley study both ndex optons and stock optons and fnd that changes n the mpled volatlty of S&P 500 ndex optons (ndvdual stock optons) are most affected by demand for ndex puts (ndvdual stock calls). They suggest that net buyng pressure s related to nvestor speculatve or hedgng demand for optons. Put optons are wdely used for downsde protecton especally out-of-the-money puts, whch are low-cost hedgng nstruments. Call optons provde upsde potental; thus, out-of-the-money calls are more lkely used for speculaton. Therefore, we attempt to determne whether ETF optons are used more often for speculatve or hedgng purposes a queston that, to the best of our knowledge, has not been explored n pror studes. Index optons are wdely used for hedgng purposes (Evnne and Rudd, 1985). Whle Moran 36

The Internatonal Journal of Busness and Fnance Research Volume 5 Number 4 2011 (2003) suggests that ETFs are also wdely used for hedgng, the speculatve motve for tradng cannot be ruled out. We nvestgate ths queston by examnng the behavor of both calls and puts of varyng levels of moneyness. The level of open nterest provdes some ndcaton of the demand for an opton. Therefore, we perform multvarate regressons to determne whether the mpled volatlty of ETF and ndex optons s related to open nterest n the manner suggested by the net buyng pressure hypothess. Our paper s related to studes by Chan, Cheng, and Lung (2004) and Kang and Park (2008). Chan, Cheng, and Lung use the Bollen and Whaley (2004) net buyng pressure metrc to examne the mpled volatltes, premums, and profts of Hong Kong Hang Seng ndex optons. Kang and Park use the net buyng pressure metrc to examne the mpled volatltes of KOSPI 200 optons. In another work, Chan, Cheng, and Lung (2006) study Hang Seng ndex optons durng the Asan Fnancal Crss and fnd evdence n support of the net buyng pressure hypothess. We also account for transacton costs. Peña, Rubo, and Serna (1999) use the bd-ask spread as a proxy for transacton costs and fnd that the spread nfluences the curvature of the volatlty smle. DATA AND METHODOLOGY We study three ETFs: Spders (SPY), Damonds (DIA), and Cubes (QQQQ after the swtch from AMEX to NASDAQ on 12/1/2004, and QQQ before the swtch). Data for these ETFs and for the S&P 500 ndex are obtaned from the Center for Research n Securty Prces (CRSP). Data for the Dow Jones Industral Average are obtaned from Dow Jones Indces webste (http://djndexes.com), and data for the NASDAQ 100 ndex are obtaned from the NASDAQ Indces webste (http://dynamc.nasdaq.com). One potental problem wth our data s that closng ndex levels are reported as of 4:00 p.m., whle ETFs contnue tradng untl 4:15 p.m. Thus, to algn the tradng perods, we use the NYSE Trade and Quote (TAQ) database to obtan the last prce for each of our ETFs wthn one second of 4:00 p.m. each day. Our sample perod s from 3/10/1999 to 12/29/2006. We use optons data from the Chcago Board Optons Exchange (CBOE) from 2003 to 2006 provded by DeltaNeutral.com. Index optons for the Dow 30, S&P 500, and NASDAQ 100 are all European and expre on the Saturday followng the thrd Frday of the expraton month. However, the ETF optons are Amercan. The data from DeltaNeutral.com ncludes mpled volatltes based on the Black-Scholes opton prcng model. Whle ths s correct for ndex optons, whch are European, t s ncorrect for ETF optons, whch are Amercan. Thus, we compute a new set of mpled volatltes for ETF optons based on a 100-step bnomal tree model. The optons dataset s fltered based on the crtera suggested by Day and Lews (1988) and Xu and Taylor (1994). The optons used to form the sample are requred to meet the followng crtera: a) The tme to expraton must be greater than 7 days and less than 30 days. δt rt b) The opton must satsfy the European opton boundary condtons, c < Se Xe and rt δt p < Xe Se. c) The opton must also satsfy the Amercan opton boundary condtons, C < S X and P < X S. d) The opton must not be so deep out of or n the money that exercse s ether mpossble or absolutely certan;.e., the absolute value of the opton s hedgng delta s between 0.02 and 0.98. After applyng these flters, we sort the remanng optons n the sample by mpled volatlty and remove those observatons n the top and bottom 1 percent, resultng n a fnal sample of 87,588 ETF optons and 105,679 ndex optons. These crtera ensure that the opton prces used n ths study are reasonable and help to avod the problems of thn tradng and excessve volatlty, whch mght endanger the soundness of our conclusons. We determne each opton s moneyness usng the Bollen and Whaley (2004) method based on the optons delta, as shown n Table 1. 37

S. I. Ivanov et al IJBFR Vol. 5 No. 4 2011 Table 1: Bollen and Whaley Classfcatons of Moneyness Based on Opton s Delta Category Labels Range 1 Deep-n-the-money (DITM) call 0.875 < C 0.98 Deep-out-of-the-money (DOTM) put 0.125 < P 0.02 2 In-the-money (ITM) call 0.625 < C 0.875 Out-of-the-money (OTM) put 0.375 < P 0.125 3 At-the-money (ATM) call 0.375 < C 0.625 At-the-money (ATM) put 0.625 < P 0.375 4 Out-of-the-money (OTM) call 0.125 < C 0.375 In-the-money (ITM) put 0.875 < P 0.625 5 Deep-out-of-the-money (DOTM) call 0.02 < C 0.125 Deep-n-the-money (DITM) put 0.98 < P 0.875 Ths table shows Bollen and Whaley s fve moneyness categores. To nvestgate the potental dfference n the mpled volatlty functons of ndex optons versus stock optons, we consder several possble explanatons: 1. ETFs and ndces have dfferent return dstrbutons as argued by Baksh et al. (2003). 2. Demand, as measured by open nterest, s dfferent for ETF optons and ndex optons. 3. Transacton costs, as measured by the bd-ask spread, are larger for ndex optons than for ETF optons. To determne whch of these explanatons are best supported by the data, we perform unvarate and multvarate tests on the mpled volatlty functon. EMPIRICAL RESULTS Frst we examne the mpled volatlty levels of ETF and ndex optons. Because ETF optons are Amercan, we compute ther mpled volatltes by usng a 100-step bnomal tree model n leu of the Black-Scholes formula. Fgure 1 presents the mean mpled volatlty for the ETF and ndex optons n each of the fve moneyness categores descrbed prevously. Results are presented separately for calls and puts. In each case, ETF optons have slghtly more pronounced volatlty smles than ther correspondng ndex optons. We also note that mpled volatltes for Damond and Cube optons are hgher n each moneyness category than for Dow 30 and NASDAQ 100 optons. For Spder/S&P 500 opton pars, the relatve levels of mpled volatlty depend on the level of moneyness. In every case, DITM ETF optons (.e., Category 1 calls and Category 5 puts) exhbt consderably hgher mpled volatlty than DITM ndex optons, even after usng a bnomal model to account for potental early exercse of ETF optons. For other categores, mpled volatlty s usually farly close for ETF vs. ndex optons, but DOTM Cube optons do have consderably hgher mpled volatlty than DOTM NASDAQ 100 optons. The documented dfference n the mpled volatltes of ETF and ndex optons mght be due to ETFs and ndces havng dfferent return dstrbutons, as suggested by Baksh et al. (2003). Alternatvely, the dfference may be explaned by transacton costs (e.g., bd-ask spreads may be larger for ndex optons compared to ETF optons) or by the demand for dfferent types of optons, as measured by ther open nterest. To address the frst of these possble explanatons, we begn by examnng hstorcal realzed daly returns of ETFs and ndces. Because Spders (Cubes) [Damonds] are desgned to be prced at 1/10 (1/40) [1/100] the level of ther trackng ndex, we scale down each ndex by ts approprate factor to facltate comparson. Table 2 shows summary statstcs usng closng prces. The average prce level and return of ETFs and ndces are very close. The volatlty, skewness, and kurtoss are smlar as well, whch suggests no sgnfcant dfference n the dstrbutons of ETFs and ndces. 38

The Internatonal Journal of Busness and Fnance Research Volume 5 Number 4 2011 In Table 3, we present the same summary statstcs usng synchronzed prces and ndex levels. Synchronzaton s performed by obtanng ntraday stock prce data from the NYSE TAQ database. Fgure 1: Mean Impled Volatltes for ETF and Index Optons Spder/S&P 500 calls Spder/S&P 500 puts 0.35 0.40 Mean Impled Volatlty (s) 0.25 0.15 0.05 Spders S&P 500 Mean Impled Volatlty (s) 0.35 0.25 0.15 0.05 S&P 500 Spders Cube/NASDAQ 100 calls Cube/NASDAQ 100 puts 0.70 0.80 Mean Impled Volatlty (s) 0.60 0.50 0.40 NASDAQ 100 Cubes Mean Impled Volatlty (s) 0.70 0.60 0.50 0.40 Cubes NASDAQ 100 Damond/Dow 30 calls Damond/Dow 30 puts 0.35 Mean Impled Volatlty (s) 0.25 0.15 0.05 Damonds Dow 30 Mean Impled Volatlty (s) 0.25 0.15 0.05 Damonds Dow 30 Ths fgure shows the Impled Volatlty Smles of the three ETFs versus ther trackng ndces. 39

S. I. Ivanov et al IJBFR Vol. 5 No. 4 2011 Table 2: Summary Statstcs for ETFs and Indces Usng Closng Prces Spder (SPY) prce 1/10 S&P 500 ndex level Spder (SPY) return S&P 500 ndex return Mean 119.6085 119.3234 02 01 Medan 120.1350 119.9080 06 04 devaton 16.6891 16.7584 0.0115 0.0113 Skewness 0.2926 0.2965 0.1843 0.1686 Kurtoss 0.5382 0.5501 2.3392 2.4259 N 1966 1966 1966 1966 Cube (QQQQ) prce 1/40 NASDAQ 100 ndex level Cube (QQQQ) return NASDAQ 100 ndex return Mean 55.2167 54.9418 00 01 Medan 39.2206 38.7200 07 09 devaton 38.7042 38.7544 0.0259 0.0255 Skewness 2.0920 2.0902 3.7728 3.9158 Kurtoss 4.2214 4.2004 84.9578 87.1130 N 1966 1966 1965 1965 Damond (DIA) prce 1/100 Dow 30 ndex level Damond (DIA) return Dow 30 ndex return Mean 102.6733 102.5845 03 02 Medan 104.6875 104.6693 05 03 devaton 9.2366 9.2876 0.0110 0.0109 Skewness 0.7532 0.7467 0.0158 0.0320 Kurtoss 0.5675 0.5568 3.6962 3.5818 N 1963 1963 1962 1962 Ths table shows the closng prces, volatlty, and returns of ETFs and ndces. Data are for the perod 3/10/1999 untl 12/29/2006. Table 3: Summary Statstcs for ETFs and Indces Usng Synchronzed Prces Spder (SPY) prce 1/10 S&P 500 ndex level Spder (SPY) return S&P 500 ndex return Mean 119.6081 119.3269 02 01 Medan 120.1850 119.9615 04 04 devaton 16.6857 16.7492 0.0114 0.0113 Skewness 0.2982 04 0.1541 0.1588 Kurtoss 0.5287 0.5434 2.4674 2.3855 N 1948 1948 1947 1947 Cube (QQQQ) prce 1/40 NASDAQ 100 ndex level Cube (QQQQ) return NASDAQ 100 ndex return Mean 54.9223 55.1998 01 01 Medan 38.6900 39.2070 07 07 devaton 38.6966 38.6456 0.0255 0.0259 Skewness 2.0914 2.0930 3.9800 3.8039 Kurtoss 4.2195 4.2414 89.6180 85.3869 N 1949 1949 1948 1948 Damond (DIA) prce 1/100 Dow 30 ndex level Damond (DIA) return Dow 30 ndex return Mean 102.6511 102.5772 03 02 Medan 104.6700 104.6662 04 03 devaton 9.2419 9.2870 0.0109 0.0109 Skewness 0.7621 0.7528 0.0495 0.0142 Kurtoss 0.5818 0.5640 3.5602 3.5510 N 1944 1944 1943 1943 Ths table shows the synchronzed prces, volatlty, and returns of ETFs and ndces. Data are for the perod 3/10/1999 untl 12/29/2006. For each of the three ETFs, the last tradng prce wthn one second of 4:00 p.m. s extracted and matched wth ts closng ndex level. In rare cases where no ETF prce s quoted wthn one second of 4:00 p.m., that day s observaton s deleted from the synchronzed dataset. The results n Table 3 are smlar to those n Table 2 n that there s no sgnfcant dfference n volatlty, skewness, and kurtoss between ETFs and ndces, whch agan shows smlarty n the return dstrbutons of ETFs and ndces. 40

The Internatonal Journal of Busness and Fnance Research Volume 5 Number 4 2011 We now test formally for equalty between the return dstrbutons of ETFs and ther correspondng ndces. Table 4 presents Kolmogorov-Smrnov values and sgnfcance levels for each of the ETF-ndex pars examned n ths study. The Kolmogorov-Smrnov test s a non-parametrc test based on the maxmum dstance between the cumulatve dstrbuton functons of two random varables. Our results show no sgnfcant dfference n the dstrbutons of ETF returns and that of ther underlyng ndces, regardless of whether we use closng or synchronzed ETF prces. We perform addtonal tests on the smlarty between dstrbutons of ETFs and underlyng ndces returns wth quantle-quantle (Q-Q) plots. In dong so, we observe that ETF and ndex returns quantles plot on a straght lne aganst each other, ndcatng that the two dstrbutons are the same. These plots are not shown but are avalable upon request. These fndngs further confrm that our observed dfferences n mpled volatltes are not due to dfferences between the underlyng ETF and ndex return dstrbutons. Table 4: Kolmogorov-Smrnov Test for Equalty of Dstrbuton Functons Usng Closng ETF Prces Usng Synchronzed ETF Prces KS value p-value Decson KS value p-value Decson Spders vs. S&P 500 0.0117 0.6536 Fal to reject 49 0.9999 Fal to reject Cubes vs. NASDAQ 100 79 0.9671 Fal to reject 64 0.9971 Fal to reject Damonds vs. Dow 30 79 0.9671 Fal to reject 87 0.9273 Fal to reject Ths table shows the Kolmogorov-Smrnov (KS) test results of closng and synchronzed ETF and ndex returns. The test has a null hypothess of equalty between the dstrbuton functons of the two seres beng compared. Data are for the perod 3/10/1999 untl 12/29/2006. We now explore alternatve explanatons for dfferences n the mpled volatlty functon. When there are lmts to arbtrage, t s possble that mpled volatlty may be related to the demand for an opton, as suggested by Bollen and Whaley s (2004) net buyng pressure argument. It s also possble that dfferences n bd-ask spreads may be partly responsble for dfferent mpled volatlty levels. To test these two predctons, we estmate the multvarate regresson model: ˆ σ = β + β OpInt 0 + β OpInt * DummyIndex 5 1 + β BdAsk + β ExpratonTme + β DummyIndex 2 3 + ε, 4 (1) where σˆ s the opton s mpled volatlty, OpInt s open nterest dvded by 1,000,000, BdAsk s the percentage bd-ask spread (calculated as the dollar spread dvded by the ask prce), ExpratonTme s the amount of tme untl opton expraton, and DummyIndex s equal to 1 for ndex optons and 0 for ETF optons. Table 5 presents regresson results for opton categores 1 and 5 (DITM and DOTM optons). Results for other categores are not reported but are avalable from the authors upon request. Gven that open nterest s a proxy for demand, we would expect ths varable to be postvely related to an opton s prce (and therefore, ts mpled volatlty). However, ths s not the case; we document a consstently negatve and sgnfcant relaton between open nterest and mpled volatlty. Therefore, our regresson results do not appear to provde evdence for the net buyng pressure theory of Bollen and Whaley (2004). The sgnfcant relaton between the bd-ask spread and mpled volatlty supports the argument that the volatlty smle s related to transacton costs. However, the drecton of ths relatonshp s not the same n each case. In general, mpled volatlty s negatvely related to percentage spreads for DITM optons, but postvely related for DOTM optons. The sgns and sgnfcance levels of the DummyIndex coeffcents confrm that on average, ndex optons have lower mpled volatltes than ETF optons. Ths s especally true for DITM optons. Although we dd not obtan the expected sgn for the open nterest regresson varable n Table 5, t s worth notng that open nterest s an mperfect proxy for net buyng pressure snce the level of open nterest s affected by both buyer- and seller-ntated trades. Therefore, t s stll possble that the demand 41

S. I. Ivanov et al IJBFR Vol. 5 No. 4 2011 for dfferent opton types may have a nontrval mpact on mpled volatltes. It s not surprsng that the greatest mpled volatlty dfferences are noted for DITM and DOTM optons. DOTM optons are especally useful for speculators due to the hgh elastcty of ther premum wth respect to the underlyng asset prce or ndex level. However, DOTM puts and calls can also be useful for hedgng by establshng floors on long postons and caps on short postons, respectvely. In addton, DITM optons can be very useful for establshng delta-neutral hedges; because ther gammas are near zero, t s not necessary to adjust the hedge rato as often when the value of the underlyng asset changes. The dfference n the mpled volatlty functons noted n Fgure 1 shows that ETF and ndex optons are not perfect substtutes for each other. Although more research s needed n ths area, ther overall hgher mpled volatltes suggests that ETF optons may be more attractve nstruments to hedgers and speculators. Table 5: Regresson Results on the Impled Volatlty Panel A: Category 1 (DITM call, DOTM put) Spder/S&P 500 calls Cube/NASDAQ 100 calls Damond/Dow 30 calls Coeffcent p-value Coeffcent p-value Coeffcent p-value Intercept 0.5840*** <.0001 1.1453*** <.0001 0.4943*** <.0001 OpInt 5.4610*** <.0001 3.0671*** <.0001 8.9034*** <.0001 BdAsk 6.5819*** <.0001 7.8635*** <.0001 2.1254*** <.0001 ExpratonTme 73*** <.0001 0.0141*** <.0001 57*** <.0001 DummyIndex 0.0384*** <.0001 0.2199*** <.0001 0.0605*** <.0001 OpInt*DummyIndex 5.1483*** <.0001 35.3780*** <.0001 5.4452*** <.0001 Adjusted R 2 0.5379 0.2757 0.3725 Observatons 11439 9624 8088 Spder/S&P 500 puts Cube/NASDAQ 100 puts Damond/Dow 30 puts Coeffcent p-value Coeffcent p-value Coeffcent p-value Intercept 0.2154*** <.0001 0.3242*** <.0001 66*** <.0001 OpInt 0.9303*** <.0001 0.1805*** <.0001 1.9325*** <.0001 BdAsk 0.0241*** <.0001 0.1267*** <.0001 0.0834*** <.0001 ExpratonTme 02*** 15 29*** <.0001 04*** 07 DummyIndex 0.0117*** <.0001 0.0284*** <.0001 0.0299*** <.0001 OpInt*DummyIndex 0.8439*** <.0001 0.9001*** <.0001 1.5635*** <.0001 Adjusted R 2 0.0432 0.3580 0.1222 Observatons 11572 8197 10619 Panel B: Category 5 (DOTM call, DITM put) Spder/S&P 500 calls Cube/NASDAQ 100 calls Damond/Dow 30 calls Coeffcent p-value Coeffcent p-value Coeffcent p-value Intercept 0.1628*** <.0001 0.4688*** <.0001 97*** <.0001 OpInt 0.4040*** <.0001 0.9929*** <.0001 4.3334*** <.0001 BdAsk 47** 0.0496 0.0692*** <.0001 0.0286*** <.0001 ExpratonTme 18*** <.0001 79*** <.0001 19*** <.0001 DummyIndex 58*** 26 0.1342*** <.0001 0.0303*** <.0001 OpInt*DummyIndex 0.0768 0.3802 0.8588*** <.0001 3.7567*** <.0001 Adjusted R 2 39 0.4449 0.0772 Observatons 6262 8579 7581 Spder/S&P 500 puts Cube/NASDAQ 100 puts Damond/Dow 30 puts Coeffcent p-value Coeffcent p-value Coeffcent p-value Intercept 0.6429*** <.0001 1.0959*** <.0001 0.5777*** <.0001 OpInt 2.8990*** <.0001 4.1980*** <.0001 9.6072*** <.0001 BdAsk 8.5135*** <.0001 8.4264*** <.0001 3.5049*** <.0001 ExpratonTme 79*** <.0001 0.0119*** <.0001 62*** <.0001 DummyIndex 0.0216*** <.0001 0.2254*** <.0001 0.0621*** <.0001 OpInt*DummyIndex 4.0745*** <.0001 34.9441*** <.0001 8.0899*** <.0001 Adjusted R 2 0.6132 0.4037 0.4236 Observatons 12979 14124 7298 Ths table shows regresson results based on equaton (1). The tme perod s from January 2003 to December 2006. OpInt s open nterest dvded by 1,000,000; BdAsk s the dollar bd-ask spread dvded by the ask prce; ExpratonTme s the amount of tme to opton expraton; DummyIndex s 1 for ndex optons and 0 for ETF optons. *, **, *** ndcate sgnfcance at the 10, 5, and 1 percent levels respectvely. 42

The Internatonal Journal of Busness and Fnance Research Volume 5 Number 4 2011 CONCLUSION In ths paper we study a popular nvestment vehcle that has recently grown n promnence, the exchangetraded fund. Optons on ETFs are a recent development and as such have not been extensvely studed. We document that there s a dfference between the mpled volatltes of ETF and ndex optons. However, we fnd no evdence of a dfference n the return dstrbutons of ETFs versus ther trackng ndces, contrary to the predctons of Baksh et al. (2003). Because the underlyng return dstrbutons are the same, we nvestgate other possble explanatons for dfferences n the mpled volatlty functons. We fnd that mpled volatlty s related to the percentage bd-ask spread, although the drecton of ths relatonshp vares dependng on the opton s moneyness. We also nvestgate Bollen and Whaley s (2004) net buyng pressure argument. We fnd that mpled volatlty s related to open nterest (our proxy for opton demand), but not n the expected drecton. However, gven that open nterest s an mperfect measure of net buyng pressure, we cannot rule out Bollen and Whaley s explanaton altogether. Our fndngs do ndcate that ETF optons have more pronounced volatlty smles than ther equvalent ndex optons. Ths s drven prmarly by the fact that DITM (and, to a lesser extent, DOTM) ETF optons have hgher mpled volatltes. Although the precse reasons for ths are stll unknown, t s plausble that n some cases ETF optons may be more attractve nstruments for hedgng and speculaton. In any event, t s clear that they are not perfect substtutes for ndex optons. The paper has a natural lmtaton n the selecton of open nterest as a proxy for opton demand. Opton demand could be better measured wth the exact net buyng pressure varable computed usng the Bollen and Whaley procedure, whch utlzes ntraday opton data. However, gven that our dataset provdes only end-of-day opton prces, the computaton of the exact net buyng pressure metrc s not possble at ths stage. In a future study, we plan to address ths ssue after acqurng the ntraday opton data. Another nterestng extenson of ths paper would be a more detaled examnaton of Cube optons. Cubes swtched tradng from AMEX to NASDAQ on 12/1/2004, and n a future paper we plan to examne how ths change affected the mpled volatlty of the correspondng ETF and ndex optons. REFERENCES Baksh, G., Kapada, N., and Madan, D. (2003), Stock Return Characterstcs, Skew Laws, and the Dfferental Prcng of Indvdual Equty Optons. Revew of Fnancal Studes, 16(1), 101-143. Bollen, N.P.B. and Whaley, R.E. (2004), Does Net Buyng Pressure Affect the Shape of Impled Volatlty Functons? Journal of Fnance, 59(2), 711-753. Chan, K.C., Cheng, L.T.W., and Lung, P.P. (2004), Net Buyng Pressure, Volatlty Smle, and Abnormal Proft of Hang Seng Index Optons. Journal of Futures Markets, 24(12), 1165-1194. Chan, K.C., Cheng, L.T.W., and Lung, P.P. (2006), Testng the Net Buyng Pressure Hypothess Durng the Asan Fnancal Crss: Evdence From Hang Seng Index Optons. Journal of Fnancal Research, 29(1), 43-62. Chrstensen, B.J. and Prabhala, N.R. (1998), The Relaton Between Impled and Realzed Volatlty. Journal of Fnancal Economcs, 50(2), 125-150. Day, T.E. and Lews, C.M. (1988), The Behavor of the Volatlty Implct n the Prces of Stock Index Optons. Journal of Fnancal Economcs, 22(1), 103-122. 43

S. I. Ivanov et al IJBFR Vol. 5 No. 4 2011 Engle, R. and Sarkar, D. (2006), Premums-Dscounts and Exchange Traded Funds. Journal of Dervatves, 13(4), 27-45. Evnne, J. and Rudd, A. (1985), Index Optons: The Early Evdence. Journal of Fnance, 40(3), 743-756. Kang, J., and Park, H. (2008), The Informaton Content of Net Buyng Pressure: Evdence from the KOSPI 200 Index Opton Market. Journal of Fnancal Markets, 11(1), 36-56. Moran, M.T. (2003), Managng Costs and Rsks wth ETF Tools. Investment Gude Seres: Gude to Exchange-Traded Funds II, 14-27. Peña, I., Rubo, G., and Serna, G. (1999), Why Do We Smle? On the Determnants of the Impled Volatlty Functon. Journal of Bankng and Fnance, 23(8), 1151-1179. Pontff, J. (1997), Excess Volatlty and Closed-End Funds. Amercan Economc Revew, 87(1), 155-169. Poterba, J.M. and Shoven, J.B. (2002), Exchange-Traded Funds: A New Investment Opton for Taxable Investors. Amercan Economc Revew, 92(2), 422-427. Xu, X. and Taylor, S.J. (1994), The Term Structure of Volatlty Impled by Foregn Exchange Optons. Journal of Fnancal and Quanttatve Analyss, 29(1), 57-74. ACKNOWLEDGEMENT We would lke to thank the journal edtors, Terrance Jalbert and Mercedes Jalbert, two anonymous referees, and partcpants at the Southwestern Fnance Assocaton and Mdwest Fnance Assocaton meetngs for ther nsghtful comments. Any errors are our own. BIOGRAPHY Dr. Stoyu Ivanov s an Assstant Professor of Fnance at San Jose State Unversty. He can be contacted at: Accountng and Fnance, BT 958, One Washngton Square, San Jose, CA 95192-0066. Phone: 408-924-3934. Emal: Stoyu.Ivanov@sjsu.edu. Dr. Jeff Whtworth s an Assstant Professor of Fnance at the Unversty of Houston-Clear Lake. He can be contacted at: 2700 Bay Area Blvd., Houston, TX 77058. Phone: 281-283-3218. Emal: WhtworthJ@uhcl.edu. Dr. Y Zhang s an Assstant Professor of Fnance at Prare Vew A&M Unversty. She can be contacted at: Department of Accountng, Fnance & MIS, College of Busness, Mal Stop 2310, T.R. Solomon St. Hobart Taylor Bldg, Rm1B118, Prare Vew, TX 77426. Phone: 936-261-9219. E-mal: yzhang@pvamu.edu. 44