A Note on the Impact of Options on Stock Return Volatility. Nicolas P.B. Bollen

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1 A Noe on he Impac of Opions on Sock Reurn Volailiy Nicolas P.B. Bollen ABSTRACT This paper measures he impac of opion inroducions on he reurn variance of underlying socks. Pas research generally finds a significan reducion in sock reurn variance following he lising of opions hrough Using a more exensive sample, I compare changes in he reurn variance of opioned socks o changes in he reurn variance of a conrol group. Since he average change in he conrol group is saisically indisinguishable from he average change in he opioned socks, I conclude ha opion inroducions do no significanly affec sock reurn variance. JEL classificaion: G18. Key words: opion lising, derivaives. Curren Version: November 1997 Previously iled The Impac of Opion Inroducion on Sock Reurn Volailiy: A Defense of he Null Hypohesis. Assisan Professor, David Eccles School of Business, Universiy of Uah, Sal Lake Ciy, UT Phone (801) Fax (801) The Chicago Board Opions Exchange generously supplied opion lising daa used in his sudy. The suggesions of Giorgio Szegö and wo anonymous referees have grealy improved he paper. Thanks also o seminar paricipans a Duke Universiy and he 1995 FMA annual meeing. In addiion, David Hsieh, Chris Kirby, Tom Smih, and Rober E. Whaley provided many helpful commens.

2 A Noe on he Impac of Opions on Sock Reurn Volailiy The recen specacle of derivaives-relaed lawsuis and bankrupcies has recharged he debae regarding derivaives regulaion. One popular quesion is wheher derivaives affec he volailiy of relaed markes. Pas research, focusing primarily on socks and sock opions, generally finds a significan reducion in he reurn variance of underlying socks following opion inroducions hrough Using a subsanially larger sample of opion lisings, I demonsrae ha a conrol group exhibis an average change in variance ha is saisically indisinguishable from he average change in opioned socks. I conclude ha opion lisings do no significanly affec sock reurn variance. These resuls shed new ligh on previous sudies of he impac of opion lisings on sock variance. 1 Trennepohl and Dukes (1979) esimae beas for opioned and non-opioned socks for he periods and and find ha he beas of opioned socks decrease more han he beas of non-opioned socks. Skinner (1989) finds ha oal sock reurn variance falls by an average of 4.8% afer opions are inroduced. Conrad (1989) esimaes ha excess reurn variance decreases from 2.29% for 200 days prior o lising o 1.79% for 200 days afer lising. Bansal, Prui, and Wei (1989) find ha variance drops by 6.4% afer opions are lised, while Damadoran and Lim (1991) deec a drop of 20%. Alhough heir samples, mehods, and esimaes vary, previous sudies generally find ha opion lisings are followed by a decrease in he reurn variance of underlying socks. This paper s conclusion differs from hose of previous sudies. The exensive sample I use provides srong evidence ha opioned socks behave no differenly han a conrol group. I show ha marke-wide variance was relaively sable for he opion lisings in he pre-1987 period examined by earlier sudies, bu ha marke-wide variance increased significanly, on average, for he opion lisings in he period. In boh periods, socks wih opion inroducions exhibi an average change in 1

3 variance ha is equivalen o he average change in a conrol group. The robus abiliy of he conrol group o mach he changes in he opioned socks leads me o conclude ha opions do no affec sock reurn variance. The remainder of his paper is organized as follows. Secion 1 discusses possible heoreical reasons for changes in sock reurn variance following opion inroducions. Secion 2 explains he empirical mehodology used o measure changes in variance. Secion 3 describes he daa used in he sudy. Secion 4 presens and discusses empirical resuls. Secion 5 concludes. 1. Theoreical reasons for changes in variance In a world of complee markes and no ransacion coss, any new securiy can be synhesized from exising securiies. Consequenly, he inroducion of opions should have no effec on underlying asses. As Grossman (1988) makes clear, however, he exisence of ransacion coss and incomplee markes suggess he possibiliy ha opions can have an impac. Grossman uses a heoreical framework o assess he informaional conen of a raded opion relaive o is synheic counerpar, and concludes ha derivaives migh affec he variance of underlying asses. The empirical quesion posed by his paper is wheher sock reurn variance changes afer opions are inroduced. Researchers provide a leas one reason why one could expec an increase in he variance of sock reurns following opion inroducions. Nahan Associaes (1969) warn ha "diversion of speculaive ineres o he opions marke" could reduce sock rading. If he inroducion of an opion lures significan rading volume away from he underlying sock, he reducion in liquidiy migh increase he sock s reurn variance. However, sudies by Bansal, Prui and Wei (1989), Skinner 1 See a survey by Damadoran and Subrahmanyam (1992) for more deail. 2

4 (1989), and Damadoran and Lim (1991) all find increases in sock rading volume following opion lisings. Researchers also sugges a leas hree reasons why one could expec a reducion in he variance of sock reurns following opion inroducions. Firs, in order for opion exchanges o lis an opion, he underlying sock mus mee cerain crieria. As noed by Skinner (1989) and ohers, he selecion crieria migh resul in a biased sample wih expeced reducions in sock reurn variance afer opions are lised. Exchange officials have indicaed ha unusually high or rising variance is a crierion for selecing socks on which o lis opions. If variance were mean revering, one would expec i o rever o is mean some ime afer opion inroducion. This may resul in a correlaion beween opion lisings and reducions in he reurn variance of underlying socks. Second, he inroducion of opions may arac new informed raders o rade. Black (1975) noes ha he financial leverage provided by sock opions can lower ransacion coss, hereby aracing oherwise unprofiable informed rades. Opions could also arac informed rades by enabling more efficien rading on negaive informaion han is possible in he sock marke. Evidence suggess, however, ha innovaions in sock prices originae in he sock marke, no he opion marke, indicaing ha informed raders prefer he sock marke. Sephan and Whaley (1990) repor ha price changes in he sock marke lead he opion marke by as much as fifeen minues. 2 Also, Fleming, Osdiek, and Whaley (1996) show ha he relaive illiquidiy of he opion marke creaes a price effec for block rades, such ha an informed rader would raionally prefer he sock marke. Third, as discussed by Fedenia and Grammaikos (1992), bid-ask spreads in he sock markes could narrow afer opion lisings, hereby reducing he bid-ask bounce in sock prices and he variance 2 See Chan, Chung and Johnson (1993) who confirm and reinerpre Sephan and Whaley's resuls. 3

5 of sock reurns. The inroducion of opions migh allow marke makers o hedge heir risks more efficienly, allowing hem o narrow he spreads hey charge. In summary, here are several heoreical argumens supporing he hypohesis ha opion inroducions migh affec underlying sock reurn variance. To es wheher variance does in fac change, he null hypohesis in his paper is ha he lising of an opion has no effec on he underlying sock s reurn variance. 2. Empirical mehodology I esimae he change in oal sock reurn variance afer opions are inroduced in order o measure he impac of opion rading on sock reurn variance. To deermine wheher opions are he cause of observed changes in variance, I use a conrol group of socks o accoun for marke-wide and indusry-wide influences. I consruc he conrol group of socks by maching he opioned socks onefor-one wih conrol socks in he same rading locaion and indusry, as idenified by he firs wo digis of he SIC code. If he conrol group exhibis an average change in variance ha equals he average change in he opioned sample, hen I can conclude ha opion lisings do no, on average, affec sock reurn variance. The marke model saes ha he reurn on sock i can be expressed as a linear funcion of he marke s reurn: Ri, = α + βrm, + ε ε ~ ( 0, σ 2 ). (1) To es for shifs in reurn variance, I incorporae an indicaor variable I ha equals zero for observaions recorded before opion lising and uniy oherwise. The model of reurns I esimae can be expressed as follows: 4

6 Ri, = α + βrm, + ε ε ~ ( 0, σ0 + σ1 I ). Under he null hypohesis ha opion lisings have no effec on sock rading, σ (2) should equal zero. The model in equaion (2) resrics he firm s α and β o be consan. Neiher Skinner (1989) nor Bansal, Prui, and Wei (1989) find evidence ha β shifs when opions are inroduced. Though Conrad (1989) repors a price effec wihin a five day period around opion lising, here is no reason o expec mean reurns o be affeced. Since here is no empirical or heoreical suppor for shifs in α and β, I esimae heir average values over he measuremen period. I use Hansen s (1982) G.M.M. o esimae parameers. G.M.M. provides hree benefis. Firs, a variance-covariance marix of parameer esimaes is generaed, hereby permiing rigorous inference regarding he significance of he change in reurn variance. Second, as will be clear, parameer esimaion is naurally accomplished using momen condiions in a G.M.M. framework. Third, he only disribuional assumpions necessary are ha sock reurns are saionary and ergodic. The model of reurns specified in equaion (2) imposes he following resricions on he daa: where and E L c c R N M c R R R i, µ h h h µ R i, m, 2 2 i, µ σ 2 2 i, µ σ I O Q P = µ = α + βr,, m σ = σ + σ I. 0 1 L0 O 0 0 N M Q P 0, (3) 5

7 Under he assumpions of saionariy and ergodiciy, he sample momens should be close o he populaion momens. Define g T bθg as he vecor of sample momens, where T denoes he sample size and θ denoes he parameer vecor. The sample approximaion of he expecaions in equaion (3) can be expressed as: g T L NM T 1 Ri, µ ( θ) =. T = 1 M O QP (4) To esimae he parameers, values are chosen which se he sample momens as close o zero as possible. In equaion (4), he sysem is jus-idenified, so parameer values exis which will se g T bθgequal o zero. The values are in fac idenical o OLS esimaes, bu he sandard errors are no. (See Hansen (1982)). I consruc es saisics based on he parameer esimaes known asympoic disribuions and verify heir small sample properies using simulaed daa. 3 Previous sudies have recognized he poenial problems in inference caused by cross-secional dependence among conemporaneous measuremens of reurns and variances for socks wih opions lised on he same dae. I incorporae cross-secional dependence in ess of significan change in variance for individual socks by grouping hose socks wih opions lised on he same dae and using he variance-covariance marix of he grouped socks parameer esimaes. To esimae he join disribuion, I simply expand he vecor of sample momens as follows: g T 1 Rk, µ k, ( θ, θ, θ,...) =, T = 1 Rl, µ l, M M P T j k l L M N R µ j, j, O P Q (5) where he subscrips j, k, and l indicae parameers of socks j, k, and l. 3 These simulaion experimens show ha he small sample properies of he es saisics are quie good. Resuls are available from he auhor. 6

8 3. Daa The Chicago Board Opions Exchange supplied a hisory of 1,942 opion lisings on domesic exchanges hrough July 30, Records wih omied or ambiguous informaion were eliminaed from he sample. In addiion, lisings ha occurred afer December 31, 1992 were excluded from he sudy since one year of pos-even daa is required for analysis. Daily sock daa were exraced from he Cener for Research in Securiy Prices 1994 NYSE-AMEX and Nasdaq apes. The final sample includes 745 NYSE-AMEX socks and 265 Nasdaq socks, all wih no missing observaions of reurns. Opion lisings for Nasdaq socks do no begin unil Thus, o he exen ha sock reurn disribuions are affeced by ime-varying variables such as he marke reurn, he Nasdaq sample should exhibi behavior differen han he NYSE-AMEX sample. The average firm from he NYSE- AMEX sample also differs subsanially from he average firm in he Nasdaq sample due o he compeiive srucure of he sock exchanges. As seen in able 1, he average Nasdaq sample sock has a larger bea and variance and a smaller size (dollar value of ousanding shares on he lising dae) han he average NYSE-AMEX sample sock. I consruc he conrol group by maching each sock in he sample group one-for-one wih anoher sock wihin he same rading locaion. Each conrol sock seleced is in he same indusry as is paired sample sock, as idenified by he firs wo digis of he SIC code. The conrol sock is rejeced if i has an opion lised wihin a four year window surrounding he sample sock s opion inroducion. Table 1 compares he average sample and conrol socks. For boh he NYSE-AMEX and Nasdaq 4 A regulaory relaxaion of lising crieria enabled exchanges o lis opions on Nasdaq socks in

9 socks, he opioned sample has a higher bea han he conrol group. 5 The sample and conrol group socks also differ along he size dimension. The average NYSE-AMEX sock in he sample is abou 36% larger han he average NYSE-AMEX conrol sock, whereas he average Nasdaq sock in he sample is abou 7% smaller han he average Nasdaq conrol sock. Though size is ofen cied as a deerminan of sock reurn volailiy, here is no compelling reason why size should affec changes in volailiy. For his reason, I do no incorporae size in my analysis Resuls I esimae parameers for he marke model using 500 daily observaions cenered around he opion lising daes. In order o incorporae possible correlaion among socks wih lisings occurring on he same dae, parameers were esimaed joinly for hose socks wih shared lising daes, as described in secion 2. Of he 1,010 lisings in he sudy, 662 occurred on a dae wih a leas one oher lising. These 662 lisings occurred on 169 unique daes, 140 for he NYSE-AMEX socks and 29 for he Nasdaq socks, wih he number of lisings per dae ranging from 2 o 15. Parameers for he remaining 348 opion lisings were esimaed individually. All parameer esimaes are esed for significance using heir asympoic normal disribuion. The number and percenage of he 1,010 opion lisings in he full sample which rejec he null hypohesis ha changes in variance equal zero are lised in panel A of able 2. Resuls are broken down by rading locaion of he underlying sock. Under he null hypohesis, one would expec significan changes in variance o appear a he rae of he significance level. However, he es for significan change in reurn variance rejecs he null hypohesis much more frequenly, boh in he combined 5 As discussed by Skinner (1989) and ohers, opions exchanges are more likely o lis opions on large and risky socks. 6 Unrepored regressions show ha firm size is no correlaed wih changes in variance following opion lisings. 8

10 sample and in he rading locaion subsamples. In he combined sample, for example, 46% of he evens in he sample group winessed a change in variance significan a a 5% level. The conrol group rejecs he null hypohesis 43% of he ime. 7 Though variance changes significanly for many opion inroducions, variance changes jus as frequenly for he conrol group. A generalized likelihood raio es for a significan difference in he sample and conrol group s rejecion raes fails: under he null hypohesis ha he rejecion raes are he same, he saisic would generae a more exreme value 65% of he ime. The average parameer esimaes of he 1,010 evens are also lised in panel A of able 2. The esimaes of average iniial variance and average change in variance are annualized by muliplying by 252, represening he approximae number of rading days in a year. The average iniial variance is 16% for he full sample and 20% for he conrol group. Mos of his difference occurs in he Nasdaq subsample. The average change in variance is 0.38% for he full sample 0.44% for he conrol group. A -es fails o rejec he null hypohesis ha he populaion average change is in fac equal across he wo groups. The average percenage change is 19% for he combined sample and 21% for he conrol group. Though he average percenage change in variance is quie differen from zero, a -es again fails o find a significan difference beween he wo average changes. This evidence indicaes ha he average impac of opion inroducions on variance is insignifican, since a conrol group exhibis changes in variance ha mach he changes in he opioned socks. This conclusion differs from hose of previous sudies. Skinner, for example, repors an average percenage reducion in oal variance of 4.8% upon opion inroducion, and an average percenage reducion of 0.8% afer conrolling for marke variance. The difference beween Skinner s conclusion and mine is due o differences in our samples and mehodologies. To deermine where we diverge, I 7 Evidence of ime-varying volailiy is consisen wih ARCH 9 and sochasic volailiy models.

11 caegorize my resuls by ime period and rading locaion in order o selec a subsample ha mos closely maches Skinner s sample. Panel B of able 2 shows he resuls for opion lisings beween April 1973 o December 1986, a period ha corresponds o Skinner s sample. Consider he NYSE-AMEX subsample, since his sample includes only NYSE-AMEX socks. Using my mehodology, he average percenage reducion in variance for he NYSE-AMEX subsample is 3%. Using Skinner s mehodology and he NYSE-AMEX subsample, he average percenage reducion is 2%. Our mehodologies give slighly differen resuls for he same daa. Furhermore, since he repors an average percenage reducion of 4.8%, our samples of lisings of opions on NYSE-AMEX socks beween are somewha differen. Noe, however, ha he conrol group exhibis changes ha mach he opioned socks in his subsample. The average reducion in variance, for example, is 1.96% for he opioned sample and 1.60% for he conrol group. A -es fails o rejec he null hypohesis ha he wo populaion averages are in fac he same. There are wo oher reasons why my resuls differ from Skinner s. Firs, since he uses variance raios o esimae changes in variance, he focuses more on he median raio raher han he average raio, since he average raio biases he change due o Jensen s inequaliy. He repors a median reducion of 19.8% in oal variance, and a median reducion of 9.7% afer conrolling for marke variance. Since I esimae he change in variance direcly, he average change in variance is a more appropriae measure. Second, and perhaps more imporan, I show ha he mach beween he opioned sample and he conrol group is mainained for more recen opion lisings. Panel C of able 2 shows he resuls for he period spanning January 1987 o December For he NYSE-AMEX socks, he average percenage increase is 42% for he opioned sample and 39% for he conrol group. A -es for a difference in means again fails o idenify a 10

12 significan difference beween he sample and he conrol group. In fac, for every subsample lised in able 2, he sample and conrol group have average changes in variance ha are saisically indisinguishable. The mach beween he opioned sample and he conrol group is mainained over wo subperiods ha exhibi quie differen levels of change in marke variance. To illusrae his, I compue he iniial level of annual marke variance prior o each opion lising and he change in annual marke variance afer each lising. For he opion lisings in he period , he average iniial marke variance is 1.66%, he average change is -.30%, and he average percenage change is 5.5%. For opion lisings in he period , he average iniial marke variance is 1.53%, he average change is.26%, and he average percenage change is 84%. Across boh he full sample and hese wo subsamples, changes in he conrol group mach changes in he sample. This resul indicaes ha opion lisings do no affec sock reurn variance. 5. Conclusions This paper seeks o deermine wheher he inroducion of opions affecs he reurn variance of underlying socks. The heighened regulaory ineres regarding he economic impac of derivaives on relaed markes provides moivaion for he sudy. I demonsrae ha a carefully consruced conrol group exhibis changes in variance ha mach changes in he variance of opioned socks. A -es fails o rejec he null hypohesis ha he wo groups have equal average changes in variance. This evidence suppors he hypohesis ha opion lisings have no significan effec on sock reurn variance. My findings should allay some of he concerns regulaory agencies and he invesing public have abou derivaives rading. Though many issues in he regulaion of derivaives demand aenion, 11

13 such as he corporae use and abuse of derivaives, he sysemic risk in derivaives markes, and proper accouning and disclosure rules, I provide evidence ha regulaors need no be concerned abou he impac of opions on underlying socks. To he exen ha sock opions are represenaive of oher ypes of derivaives, my conclusions suppor he coninued use and developmen of derivaive markes. 12

14 References Bansal, V., S. Prui, and K. Wei, 1989, An empirical reexaminaion of he impac of CBOE opion iniiaion on he volailiy and rading volume of he underlying equiies: , Financial Review 24, Black, F., 1975, Fac and fanasy in he use of opions, Financial Analyss Journal 31, Chan, K., P. Chung, and H. Johnson, 1993, Why opion prices lag sock prices: a rading-based explanaion, Journal of Finance 48, Conrad, J., 1989, The price effec of opion inroducion, Journal of Finance 44, Damadoran, A. and J. Lim, 1991, The effecs of opion lising on he underlying socks reurn processes, Journal of Banking and Finance 15, Damadoran, A. and M. Subrahmanyam, 1992, The effecs of derivaive securiies on he markes for he underlying asses in he Unied Saes: a survey, Financial Markes, Insiuions and Insrumens 1, Fedenia, M. and T. Grammaikos, 1992, Opions rading and he bid-ask spread of he underlying socks, Journal of Business 65, Fleming, J., B. Osdiek, and R. Whaley, 1996, Trading coss and he relaive raes of price discovery in sock, fuures, and opions markes, Journal of Fuures Markes 16, Grossman, S., 1988, An analysis of he implicaions for sock and fuures price volailiy of program rading and dynamic hedging sraegies, Journal of Business 61, Hansen, L., 1982, Large sample properies of generalized mehod of momen esimaors, Economerica 50, Nabar, P. and S. Park, 1988, Opions rading and sock price volailiy, Working Paper 460, Leonard N. Sern School of Business, New York Universiy. Nahan Associaes, 1969, Public policy aspecs of a fuures-ype marke in opions on securiies. Skinner, D., 1989, Opions markes and sock reurn volailiy, Journal of Financial Economics 23, Sephan, J. and R. Whaley, 1990, Inraday price change and rading volume relaions in he sock and sock opion markes, Journal of Finance 45, Trennepohl, G. and W. Dukes, 1979, CBOE opions and sock volailiy, Review of Business and Economic Research 14,

15 Table 1 Summary Saisics The sample and conrol groups are compared. Size equals sock price muliplied by ousanding shares on he lising dae. Bea and variance are esimaed using 250 daily observaions prior o he opion lising dae. Sample and Conrol Group Summary Saisics NYSE-AMEX (745 obs.) Nasdaq (265 obs.) Combined (1,010 obs.) Sample Conrol Sample Conrol Sample Conrol Size in $000s 581, , , , , ,424 Bea Variance 12.15% 11.45% 27.07% 43.36% 16.07% 19.82% 14

16 Table 2 Changes in Sock Reurn Variance Panel A liss he number and percenage of socks wih significan changes in variance afer opions are lised. Rejecions of he null hypohesis are recorded a he 5% significance level using he asympoic normal disribuion of he parameer esimaes. Also displayed are he average annual reurn variance prior o opion lising, he average change in annual variance, and he average percenage change in annual variance afer opion lising. The ess for difference show he wo-ailed probabiliy of a larger difference beween he sample and conrol group under he null hypohesis of equaliy. Panels B and C show he resuls for wo subsamples. Panel A: Full Sample NYSE-AMEX (745 obs.) Nasdaq (265 obs.) Combined (1,010 obs.) Sample Conrol Tes Sample Conrol Tes Sample Conrol Tes # of Rejecions % Rejecions 47.52% 44.03% % 41.89% % 43.47% 0.65 Iniial Variance 12.15% 11.45% 27.07% 43.36% 16.07% 19.82% Change in Variance -0.05% 0.30% % 0.82% % 0.44% 0.95 % Change in Variance 17.10% 18.83% % 26.43% % 20.83% 0.67 Panel B: April December 1986 NYSE-AMEX (409 obs.) Nasdaq (43 obs.) Combined (452 obs.) Sample Conrol Tes Sample Conrol Tes Sample Conrol Tes # of Rejecions % Rejecions 51.34% 45.48% % 39.53% % 44.91% 0.41 Iniial Variance 12.48% 13.07% 14.82% 24.68% 12.70% 14.17% Change in Variance -1.96% -1.60% % 0.66% % -1.39% 0.95 % Change in Variance -2.98% 2.53% % 22.55% % 4.43% 0.38 Panel C: January 1987-December 1992 NYSE-AMEX (336 obs.) Nasdaq (222 obs.) Combined (558 obs.) Sample Conrol Tes Sample Conrol Tes Sample Conrol Tes # of Rejecions % Rejecions 42.86% 42.26% % 42.34% % 42.29% 0.94 Iniial Variance 11.76% 9.48% 29.45% 46.98% 18.79% 24.40% Change in Variance 2.27% 2.62% % 0.85% % 1.92% 0.93 % Change in Variance 41.55% 38.68% % 27.18% % 34.11%

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