faj hancock 1993 triple witching

8/6/2019 FAJ Hancock 1993 Triple Witching

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CFA Institute

Whatever Happened to the Triple Witching Hour?Author(s): G. D. HancockSource: Financial Analysts Journal, Vol. 49, No. 3 (May - Jun., 1993), pp. 66-72Published by: CFA InstituteStable URL: http://www.jstor.org/stable/4479651 .

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TechnicalNotesWhatever Happened to the Triple Witching Hour?

G. D. Hancock, AssistantProfessorof Finance,Schoolof BusinessAdministration,Universityof Missouri-St.LouisOnJune 19, 1987, the Chi-cago MercantileExchange(CME),he New YorkFu-turesExchange (NYFE)ndtheNew YorkStockEx-change (NYSE)hanged theexpirationday of some in-dexfuturesand selectin-dex optionsin an effort oreduce the impactof thetriplewitchinghour. SinceJune 1987, marketactivityon derivative ontractexpi-ration dayshas not beenabnormal when comparedwith trading on non-expi-rationdays.However,astherehad been no evidenceof significantpricedistor-tions prior to the change,itis difficult o conclude thattheCME hanges caused adecrease n price distor-tions.Even so, thevolatilityof returnsremains highduring expirationperiods,mostlikelybecause of theunwindingof intermarketarbitragepositions.

Index arbitrage and programtrading are popular culpritswhenever the market experi-ences periods of unusual pricepressure. Yet Famaargues thatindexarbitrage,acilitated y pro-gram rading,hould have exactlythe opposite effect: By linking

stock and futures prices, indexarbitrage should reduce thenoise in the combined signals ofthe two markets.1 Conversely,market mechanisms that reducethe efficiency of index arbitragedestroy some of the economicvalue of the futures market byincreasing the variance of dis-crepancies between stock and fu-tures prices.Abnormal stock price movementsfrequently accompany the triplewitching hour-the final hour oftrading on days when index fu-tures, index options and regularstock options expire simulta-neously. In an effort to eliminateor reduce the impact of the triplewitching hour, the Chicago Mer-cantile Exchange (CME), he NewYork Futures Exchange (NYFE)and the New York Stock Ex-change (NYSE)changed the expi-ration day of the S&P and NYSEcomposite index options and in-dex futuresexpiring in Marchcy-cle months.2Prior to June 19, 1987, the S&Pand NYSEcomposite index op-tions and index futures ceasedtrading at the close of the thirdFridayin Marchcycle months. AsTable I shows, many of the in-dexes now cease trading at theclose of the third Thursday inMarchcycle months and the rele-vant contract price is the openingprice on Friday. The change wasmade to "quell the stock marketvolatility usually sparked by thetriple witching hour."3This note investigates the impactof the changes made by the CMEon the market as a whole duringthe triple witching hour periods.In order to focus on the marketasa whole, the idiosyncraticfactorsassociated with individual stock'sreturnswill be largely ignored, as

will the market-making capacityof differentspecialists.The Impact of DerivativeMarket Activity-on the SpotMarketWhile there is little agreement onwhether the futures market hashad any long-run impact on thevolatilityof the cash market, thereis a general consensus that themarkets are interrelated and that

an expiration-day effect does ex-ist. Kling argues that the expira-tion-day phenomenon is due toweaknesses in the specialist trad-ing system.5 The main weaknesshe sees is that regulatory advan-tages given to specialists allowthem to drive other providers ofliquidity out of the market. Thiscan become a problem whenmarket participantsunwind theircovered positions at the termina-tion of trading. The close-out isfrequently in cash, so when clos-ing trades on one side of themarket predominate, a substantialorder imbalance can result in thecash market.If the specialistshan-dling the underlying stock cannotprovide sufficient liquidity, theseorder imbalances lead to sharpprice movements, either up ordown.Stoll and Whaleyexamine expira-tion-dayeffects for the period July1, 1983 through December 27,1985.6 They use a data base thatcontains hourly price observa-tions from closing the day beforeexpiration to 10:30 a.m. EST onthe day afterexpiration. Their re-sults show that volatility of pricechanges is significantly higher onexpiration days, especially duringthe last 15 minutes of trading.Theobserved price effects also appearto be associated only with theS&P 500 futures contract expira-tion, rather than the S&P500 op-tion contracts. The authors at-

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TableI Futuresand OptionsIndex SettlementUnderlying Index Exchange Trading Ends SettlementBasis

S&P500 IndexFutures CME Thursday Friday OpeningOptions on Futures CME Thursday Friday OpeningOptions (new) CBOE Thursday Friday OpeningOptions (old)* CBOE Friday FridayCloseS&P 100 IndexOptions CBOE Friday FridayCloseMajorMarketIndexFutures CBT Friday Friday CloseOptions AMEX Friday FridayCloseNYSEComposite IndexFutures (new) NYFE Thursday Friday OpeningFutures (old)* NYFE Friday Friday CloseOptions NYSE Thursday Friday OpeningValue Line IndexFutures KBOT Friday Friday CloseOptions PHSE Friday FridayClose

Source:"Money ndMarkets,"WallStreetjournal, une 12, 1987.*The ontract lasswith greater nvestorparticipation.

tribute the price effect to theadditional ost of liquidity,whichfrequently increases on expira-tion days, as well as with largeblock transactions.Stoll and Whaley also examinethe trading inks between indexfuturesand the stock market norder to evaluatemodificationsntradingprocedures hat could al-leviate marketcongestion on ex-piration days.7They discuss insome detailthe impactof switch-ing settlement rom Friday's los-ing price to Friday's openingprice.StollandWhaley rgue hat,with some modifications, uch asdisclosure of the demand andsupplysituation,he openingset-tlementmay result in more effi-cienthandlingof thelarge radingimbalances hat frequentlyoccuron expiration days.Withoutthemodifications,however, the spe-cialist retains too much discre-tion, and the order-imbalanceproblem may be compounded.Most recently, Stoll and Whaleyhave studied a two-and-one-halfyear period prior to June 1987and a two-and-one-halfear pe-riod afterJune 1987 in order todetermine whether changes inthe settlement times of certaincontractsmitigatedconcern over

the triple witching hour.8Theyexaminethe tradingvolume andpricebehaviorof all NYSE tockson all expiration days. The evi-dence indicates that expiration-dayeffectsarequitesmallon bothquarterly ndmonthlyexpirationdays.ThatStollandWhaley's e-sults are very similar to thosepresented in this note, althoughthe latterare basedon a differentdata set, strongly suggests thatregulators have overreacted toexpiration-dayffects.Feinsteinand Goetzmann nvesti-gate triple witchinghours in or-der to determinewhether theseperiodsare characterized y ex-cessive volatility.9They examinethe daily returnsof the S&P500indexfromJanuary 983 throughJune 1988, measuringhow manyexpirationdays ell abovethe me-dianvolatility nd how manybe-low. Theyfind that, prior to therule changes n 1987, riplewitch-inghour dayswere more likelytofall above the median volatilitythan below. However,after therule changes there appeared tobe a "reducedpropensityor ex-pirationFridayso exhibitunusu-ally high volatility."Of course,withsuch a smallsample,defini-tive conclusions cannot bereached.

Glossary*Index Arbitrage:A trading trategy hattakesadvantage f any violationofthe cost-of-carryrinciple. fthe spot stockindex priceandthe futuresprice aremis-aligned, or example,an indexarbitrage anconstructa tradethatearns a profitwithzeroinvestment.*Noise:Anoisy processconsistsofvariables hataredependent;that s, autocorrelation oeffi-cients are not zero.*Pooled F-Test:Atest of the relationshipbe-tweenthe averagevolatility ftwo randomvariablesat differ-ent pointsin time.*Pooled t-Test:Atest of the differencebe-tweenthe meansof two ran-domvariables akenatdiffer-ent pointsin time. The testrequiresthe use of a pooledstandard rror of the differ-ence betweenthe means.*Program Trading:Trading hat nvolvesthe useof a computer o look forprofitabledivergences romcost-of-carryelationships ndsuggestsriskarbitrageradingstrategieso profitfrom thosepricingerrors.*' Stock Market Volatility:Themagnitudeof pricechangesover a given periodof time for agivenmarket n-dex. Thelarger he magnitudeof pricechanges,as measuredby standard eviation, hehigherthe stock marketvolatility.

In a recent study using 11 quar-terlyexpirations f S&P 00indexcontractsn the periodJune1984through December 1986, Stolland Whaleystudy the expirationbehavior of individualstocks.10

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More specifically, hey examinewhether expiration-day effectssimplyreflectnormalmovementsbetween bid and askprices.Theyfind thatthe volume of trading nthe last half hour of expirationdays s substantiallybovenormaland the price behaviorof stocksthat are subjectto program rad-ing (i.e., those included in theS&P500) is verysimilar o thatofstocks that are not (i.e., thosestocks not included in the S&P500). They conclude that theprice reversals on the Mondayfollowinganexpirationday do infactreflectthe bid-ask preadsofthe individual tocks.Herbstand Maberly tudy he pe-riod June 1984 through Septem-ber 1989,comparinghe 12expi-rations prior to the June 1987changes o the 10expirationshatoccurred after the changes.11They indthat he new settlementprocedureshave significantly e-duced triplewitchinghour vola-tility,butonlyat the expenseof asignificant ncrease in first-hourvolatility.The NYSErecently proposed arule that would curb certainforms of program trading andthus reduce stock market vola-tility during expiration peri-ods. Not all agreethatvolatilitywould be reduced. For example,ChicagoBoardOptionsExchange(CBOE)officials believe that anafternoonexpirationallows in-vestors to respond to importanteconomic news, which is oftendisclosed on Fridays.To curbtrading, they argue, would in-crease investors' isk.Using minute-by-minuteash in-dex values for the period fromApril30,1987toJuly24, 1989, hisnote investigateshe triplewitch-ing hour.13To assess the degreeof uniformity f price changes nthemarket,t firstuses a variant fthe comparison-period pproachto analyzechangesin returnsonthe S&P500cash index.Then,todeterminethe overall impactofmarketprice effects,reversalsofthe S&P500 cash index are calcu-lated in expiration periods and

comparedwith reversals n non-expirationperiods.Volumeof tradingduringthe tri-ple witching hour is deempha-sized. Thegoal of thisstudy s toevaluate the price effects ratherthan the functioningof market-makers or the performance ofindividual tocks.

Comparison-PeriodApproachThe methodology s a variantofthe comparison-period pproach(CPA), irst developed by Masu-lis.14This approachuses an esti-mate of theaverage ateof returnon theS&P500 cash indexoverarepresentative eriod,designatedthecomparisonperiod.Thisaver-age rate of returnis then com-pared with the average rate ofreturnon the index aroundthetime of contract xpirations.The sample used here includesnine comparison periods andnine expirationperiods. The hy-pothesisthat riplewitchinghourexpirationsdistort he underlyingcash market an be rejectedf theaverage ateof returnon the S&P500cashindex aroundexpirationperiods does not differ signifi-cantly from the average in thecomparisonperiod.15The representative eriodis des-ignatedasthelast hourof tradingon the firstThursday ndthefirstand last hours of tradingon thefirst Friday of February cyclemonths, times in which neitherindex options nor index futurescontractsexpire. This approachholds constant the day of theweek, as well as the number ofobservations, so that any ob-served changes in the rate ofreturncan be attributedo expi-rationeffects,rather handay-of-the-weekeffects.16The triple witching hour occursduring helasthourof tradingorcontracts hatexpirein March y-cle months. The expirationdayfor index futureswas originallythe third Friday f the expirationmonth; now the indexes ceasetradingat the close of the third

Thursday of the expirationmonth. Individual tock optionscontinue radinguntilthe close ofthe third Friday.Thus the lasthour on Thursdayand the firstand last hours on Friday re eval-uated to ascertain he impactofthe expirationperiod.A secondexpiration period-when op-tions, but not futures, expire-includes the last hour of tradingon the third Thursdayand thefirstand lasthours of tradingonthe thirdFriday or contracts x-piring in January ycle months.Let the rate of returnof the S&P500 spotindex atminutet duringmonth i be denoted:ri,t = Upi,t + 1 - Pi')/Pi,t]A pooled t-test s used to test forthe equivalenceof the averageabnormalrates of returnof theexpirationperiod (ARE) nd thecomparisonperiods (ARC).17pooled F-test s used to test forthe variability f averageratesofreturn.The ARE, or month i, based onminute-by-minutendexvalues, saggregatedover the last hour oftrading or each of the nine peri-ods separately ndis given as:Eq. 1

60AREi= E ri,t/60.

t= 1

The ARE,s calculated or threeseparate time periods for bothexpirationperiods-the last hourof tradingon the thirdThursday,the last hour on the thirdFridayand the first hour on the thirdFriday. The AREis aggregatedover all nine periodsas follows:Eq. 2

9ARE ARE1/9.

i = 1Notethata separateARE xistsforeach time periodfor bothexpira-

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Table II Comparison-PeriodApproach Using 60-Minute IntervalsPart A: Triple Witching Hour (March Cycle) Returns/No-Expiration(FebruaryCycle) Returns

Last Hour On Thursday First Hour on Friday Last Hour On Fridayt = -0.9234a t = -0.0238 t = -0.2138F = 24.88b F = 60.08 F = 65.13

Part B: Options-Only-ExpirationQanuaryCycle) Returns/No-ExpirationReturns(FebruaryCycle)LastHour On Thursday FirstHour On Friday LastHour On Fridayt = -0.2506 t =-0.2602 t =-0.2469F = 27.57 F = 54.94 F = 51.77

Part C: Triple Witching Hour (March Cycle) Returns/Options-Only-ExpirationOanuaryCycle) ReturnsLastHour On Thursday FirstHour On Friday Last Hour On Friday

t= +0.7188 t= -0.0001 t= -0.0181F =2.70 F =1.71 F =3.64a. All t-testresultsare insignificantt the 5% evel.b. AllF-test esultsaresignificantt the 5% evelwith540-1degreesof freedom.tion periods (i.e., when optionsand futuresexpireand when onlyoptionsexpire).The sameproce-dure is used to obtainthe ARC,with the relevanttime periodsfallingon the first Thursday ndFriday f the February ycle.Thetest is then repeated using 15-minute tradingintervals nsteadof 60-minutetrading ntervals.18The test statisticfor equalityofmeansis denotedas:Eq. 3

ARE ARCSEp[l/Ne + 1/Nc]l/'whereSEps the pooledstandarderror of the differencebetweenmeans,definedas[(Ne - 1)Se+ (Nc -1)S

(Ne+ Nc -2)]1/2where

Ne = the number of observa-tions in the expirationperiod;NC= the number of observa-tionsin the comparisonperiod;Se = the varianceof the expi-ration-period returns;and

SC = thevariance f the com-parison-periodeturns.The pooled F-test was obtainedbytaking he ratioof Seto SCwith540-1degreesof freedom.19Table II shows the results of thepooled t-test(Equation 3)) andthe pooled F-test for each timeperiod, using 60-minutetradingintervals. The results of thepooled t-test are insignificantfor each time period, regardlessof how the expirationperiod isdefined. This indicatesthat theimpact of expiring futuresandoptions contractsis not strongenoughto cause pricedistortion.It is interesting o note that, n allbut one case, the averagerateofreturn n the comparisonperiod(ARC)s larger than the averagerate of returnin the expirationperiod (ARE).This resultis con-sistentwithprior indings hat heS&P500declinesin priceduringthe last hour of tradingpriortoexpiration.20Thisdoes not implythat all stocks in the S&P500decline.)The pooled F-testsare all signifi-cant at the 5%level (with 540-1degrees of freedom).This indi-catesthatvolatility f returnsdur-ing the expirationperiodsis sig-nificantlydifferentfrom returnvolatilityduring the comparison

period.Note that,when the expi-rationperiod is comparedwiththe option-only expirationmonths, he difference n volatili-ties is not as great as when theexpiration period is comparedwith the non-expirationperiod.The factthatvolatilitiesdiffersig-nificantlybetween time periodssuggeststhat the varianceof theS&P 500 in any given period isnot a good indicatorof its vari-ance in othertime periods.21Any ncrease n variances or themarketas a whole when deriva-tive security contracts expireprobablyreflectsan increase intrading volume from investorsunwinding heirpositionsand en-gaging n intermarketrbitrage.22This activity,however, appearsnot to cause price distortions orthe marketas a whole.The resultsin TableIII are verysimilar o those presented n Ta-ble II.TheF-test esultsare not aslarge as those presented n TableII, but they remain significant,indicating that risk differencespersist n the 15-minutentervals.This result s interesting, ecauseit is the last 15minutesof tradingthat is claimed to be the mostvolatile.These resultsdo notsup-port this claim. Furthermore,pricing discrepancies are nomore apparent n the 15-minuteintervals han n the longer inter-vals.Insummary,he expiration f de-rivative securities does not ap-pearto cause pricedistortionsorthe marketas a whole. Further-more,while there are significantdifferencesin volatilitybetweenperiodsurroundingontractxpi-rationsand otherperiods, signif-icantdifferencesn volatility xistregardlessof the time periodschosen.

ReversalsThe unwindingof arbitrageposi-tionscould puteitherupwardordownward pressure on prices.Stoll and Whaley showed thatthere aresignificantly egativeav-erage returnson the S&P500andthe S&P100 when futures and

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Table III Comparison-PeriodApproach Using 15-Minute IntervalsPart A: Triple Witching Hour (March Cycle) Returns/No-Expiration(FebruaryCycle) Returns

Last15 Mins. On Thursday First15 Mins. On Friday Last15 Mins. On Fnidayt = -1.8155a t = -0.2361 t = -0.2714F =30.99b F =1.47 F =1.89

Part B: Options-Only-Expiration JanuaryCycle) Returns/No-Expiration(FebruaryCycle) ReturnsLast15 Mins. On Thursday First15 Mins. On Friday Last15 Mins. On Fridayt = -0.2398 t =-0.2553 t =-0.2824F = 2.34 F =2.44 F =3.23

Part C: Triple WitchingHour (March Cycle) Returns/Options-Only-Expiration(JanuaryCycle) ReturnsLast15 Mins. On Thursday First15 Mins. On Friday Last15 Mins. On Fridayt = - 1.0122 t = -0.0036 t = -0.0139F =13.23 F =1.66 F =1.71a.All t-testresultsareinsignificantt the 5% evel.b. AllF-test esultsaresignificantt the 5% evelwith135-1degreesof freedom.

options expire together.23Thissuggeststhatarbitragersend tobe long in stocks and short infutures,at leastduring he periodfromJuly1,1983 hroughDecem-ber 27, 1985.If the price changeon an expira-tion day is abnormal, he pricewill tend to returnto a normallevel on the following tradingday.Ifthepricedoes notreverse,the initialpricechangemusthavebeen, we assume, the result ofnewinformation,ot theresultofunwindingarbitragepositions.Areversals defined as a change nthe sign of the rate of returnduringthe last 15 minutesof theexpiration day, compared withthe rateof returnduringthe first15 minutesof the followingtrad-ing day.Acontinuations definedas no change in the sign of theratesof returnbetweenthese pe-riods. Specifically,he returndur-ing the last 15 minutesof tradingon the expirationdayis givenas:Roj = (Pdose1-Pclose- 15,i)/

Pclose - 15,iand the return during first 15minutes of the followingtradingdayis:Rjj = (Popen + 15,i - Popen,i)/Popen,i

TableIVreports hereversals ndcontinuationsobserved on dayswhen futuresand options expire,when only options expire andwhen thereis no expiration t all.PartA comparesrates of returnduringthe last 15 minutesof therelevantThursday ith those dur-ing the first 15 minutes the fol-lowing Friday. ndex futuresandindex optionsexpire on the thirdThursday,while individual tockoptionsexpireon the thirdFridayof March ycle months.Options-only expirations re evaluated nthe January ycle.The no-expira-tion periodis definedas the firstThursday nd Fridayof the Feb-ruarycycle.The ratesof return n PartAshowthatonly one reversal ccurred nthe three time periods specified.The reversalappearsas the firstentryunder the futuresand op-tions expirationperiodandis notof a significantmagnitude.Theother entries are continuations,implying that the initial pricechange s the resultof new infor-mation,not the resultof unwind-ing arbitragepositions.Interest-ingly, here doesnot appear obeanydifference n the behaviorofreturn patternsbetween expira-tion periods and non-expirationperiods-once again suggestingno expiration-dayffect.

PartB of TableIVshows the ratesof returnduringthe last 15 min-utes of the relevantFridaycom-paredwith those in the first 15minutes of the following tradingday,withthe cyclesas definedinPartA. The resultsdiffer slightlyacross the three time periods.First,when both futuresand op-tions expire, two of the nine ex-pirations how reversals,but nei-ther is significant. Next, whenonly options expire, four of thenine periods show reversals, ndtwo are significant.Lastly,whenthereis no expiration,wo of thenine periods show reversals, neof which is significant.These findingssuggest that nter-market arbitragemay occur onFridays ccasionally, lthoughnotconsistently.But thereappears obe no discerniblepatternof arbi-trageon expirationdays,as non-expirationdaysshow reversalsaswell. Furthermore, f the eightreversalsobserved over all threeperiods, only three are of suffi-cientmagnitudeo cover transac-tion costs.

Reported Market ActivityAperusalof the WallStreetjour-nal since June 19, 1987 showsthat the markets on the thirdThursdaynd Friday f each quar-terlyexpirationperiodhavebeenunremarkable.Table V notes afew exceptions. In December1987, the market plunged by50.07 points late on the thirdThursdayf themonthandrose by50.90pointsbyclose of the follow-ing day. This market movementwas attributed o the assurancefrom Fed ChairmanGreenspanthat the October deficit was anaberration. n June of 1988, themarket fell by 37.16 points onnews of the potential nflationaryimpactof the Midwest rought. nMarch of 1989, the marketplunged by 48.57 points in re-sponse to IBM's ow earningsre-ports and increased inflationaryexpectations.The increase n theDJIAof 45.50 points in March1990 was attributed o reducedexpectations of tighter moneysupply.

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TableIV ReversalsPart A: Ratesof Return During the LastFifteen Minutes on Thursday Compared with the First Fifteen Minutes on Fridaya

Futures/Options Expiration Options-OnlyExpiration No Expiration06-18-87: 0.00748% 07-16-87: 0.003313% 04-30-87: 0.002550%06-19-87: (-0.002707%) 07-17-87: (0.013419%) 05-01-87: (0.048601%)09-17-87: 0.172950% 10-15-87: -0.349985% 08-06-87: 1.162216%09-18-87: (1.481056%) 10-16-87: -0.271502%) 08-07-87: (0.976992%)12-17-87: -1.426428% 01-14-87: -0.875227% 11-04-87: -1.691447%12-18-87: -1.517406% 01-15-87: (-0.589995%) 11-05-87: -1.634898%)03-17-88: 0.589955% 04-14-88: 0.202978% 02-04-88: 0.588954%03-18-88: (0.601979%) 04-15-88: (0.163407%) 02-05-88: (0.722091%)06-16-88: -0.033208% 07-14-88: 0.269156% 05-05-88: -0.198870%06-17-88: (-0.056868%) 07-15-88: (0.298832%) 05-06-88:(-0.239884%)09-15-88: -0.062606% 10-20-88: (0.265030% 08-04-88: 0.151625%09-16-88: (-0.022402%) 10-21-88: (0.281875%) 08-05-88: (0.117885%)12-15-88: 0.089774% 01-19-89: 0.076339% 11-03-88: 0.239187%12-16-88: (0.132551%) 01-20-89: (0.070230%) 11-04-88: (0.140964%)03-16-89: (0.558942%) 04-20-89: 0.455362% 02-02-89: 0.618865%03-17-89: (0.414887%) 04-21-89: (0.409548%) 02-03-89: (0.562582%)06-15-89: 0.623711% 07-20-89: 0.514293% 05-04-89: 0.743896%06-16-89: (0.595788%) 07-21-89: (0.505188%) 05-05-89: (0.711288%)

Part B: Rates of ReturnDuring the LastFifteen Minutes on FridayCompared with the FirstFifteen Minutes on MondaybFutures/OptionsExpiration Options-OnlyExpiration No Expiration06-19-87: 0.027880% 07-17-87: 0.039993% 05-01-87: 0.047314%06-22-87: (0.048770%) 07-20-87:(-0.018812%) 05-04-87: (0.077126%)09-18-87: -0.001476% 10-16-87: -0.359700% 08-07-87: -0.087543%09-21-87: (0.005683%) 10-19-87: -0.407055%) 08-10-87: (-0.049428%)12-18-87: 0.179739% 01-15-88: 0.166910% 11-06-87: -0.102791%12-21-87: (0.105708%) 01-18-88:(-0.016794%) 11-09-87: -0.204894%)03-18-88: -0.002198% 04-15-88: 0.000523% 02-05-88: 0.022425%03-21-88: (-0.996006%) 04-18-88: (0.019989%) 02-08-88: 0.057390%06-17-88: 0.022311% 07-15-88: 0.044139%* 05-06-88: -0.031673%06-20-88:(-0.030074%) 07-18-88:(-0.035352%) 05-09-88: (0.003216%)09-16-88: 0.058705% 10-21-88: 0.018361% 08-05-88: 0.012858%09-19-88: (0.036053%) 10-24-88: (0.022872%) 08-08-88: (0.052198%)12-16-88: 0.048305% 01-20-89: -0.006730%* 11-04-88: -0.043837%*12-19-88: (0.018061%) 01-23-89: (0.035708%) 11-07-88: (0.011232%)03-17-89: -0.150296% 04-21-89: 0.074304% 02-03-89: -0.112339%

03-20-89: (-0.052907%) 04-24-89: (0.029960%) 02-06-89: (-0.101127%)06-16-89: 0.026432% 07-21-89: 0.047863% 05-05-89: 0.050512%06-19-89: (0.051523%) 07-24-89: (0.019712%) 05-08-89: (0.059357%)a.Friday eturns rein parentheses elow the respectiveThursdayeturns.b. Mondayeturns rein parentheses elow the respectiveFriday eturns.*Magnitudef reversal ignificantt the 5% evel.

The remarkable increases or de-creases in market volatility thathave occurred around the triplewitching hour can be attributedto investor responses to new in-formation. The remaining quar-terly Thursdays and Fridays arerelatively quiet, with no report ofunusual market activity.This sug-gests that the triple witching houris not something that need be ofmajor concern and is rarely thesole source of marketstimulation.ImplicationsThe S&P 500 demonstrates nosignificant price distortions when

futures and options expire (orwhen only options expire). Theredo, however, appear to be signif-icant differences between returnvolatility during expiration peri-ods and volatility during non-expiration periods. Itappearsthatchanging the expiration dates ofoptions and futures has not beeneffective in reducing volatility to"normal" evels.The S&P 500 frequently exhibitsprice continuations rather thanreversals. This suggests that theinitial price change is a result ofnew information, rather than in-

termarketrbitrage. o the extentthat ntermarket rbitrage ctivitydoes occur,it does not appear obe associatedwithan expiration-day effect.It usuallyoccurson aFriday,perhapsbecause selectedmacroeconomicnformation uchasunemploymentndmoneysup-ply dataare systematicallyeleasedon Fridays.Concern over expiration-dayf-fectsappears o be unwarranted.Price distortionsare not evident,andincreasedvolatilitys attribut-able,in partatleast,to the incor-porationof new information.Re-

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TableV Wall StreetJournal Re-portson DJLA ctivity*Third ThirdMonth/Year Thursday Friday

June 1987 +0.78 +12.72Sept. 1987 -2.29 -3.26Dec. 1987 -50.07 +50.90March1988 +21.72 +1.33June 1988 -37.16 +9.78Sept. 1988 -8.36 +5.87Dec. 1988 -1.25 + 17.71March1989 +20.17 -48.57June 1989 -28.36 +1.38Sept. 1989 -14.63 +9.69Dec. 1989 -7.46 -14.08March 1990 +7.88 +45.50June 1990 -1.48 +7.67Sept. 1990 -39.11 -5.94Dec. 1990 +2.73 +4.20March 1991 -2.97 -3.96June 1991 -1.56 +11.62Sept. 1991 +6.48 -5.14Dec. 1991 +6.27 +20.12*A1l eclines/increaseseferto movement nthe DowJonesIndustrial verage s reportedby theWallStreetournal.

ducingvolatilitywould thereforerequire that informationsome-how be suppressedor that secu-rity prices not be allowedto re-flectnew information uickly.Footnotes1. R.j Barro, E F Fama, D. R. Fis-chel, A. H Meltzer, R W Roll andL.G. Telser,Black Mondayand theFuture of Financial Markets Home-wood, IL: rwin, 1987).2. Throughout this paper, the Marchcycle refers to the months of March,June, Septemberand December; theJanuary cycle refers to the months

ofjanuary, April,July and October;and the February cycle refers to themonths of February,May, Augustand November.3. Another change was made by bothexchanges in June 1987: Serialcontract months were added for theindex options. Index options expireon the thirdFriday of all expirationmonths except those months in theMarch cycle. See S. McMurrayandB. E Garcia, "WaryTradersForeseeConfusion as Triple WitchingTimeLooms,"Wall Street Journal June12, 1987.4 For an in-depth comparison of thereaction of individual stocks in theS&P500 versus non-S&P500stocks, see H R. Stoll and R. Whaley,

"Program Trading and ExpirationDay Effects,"Financial AnalystsJour-nat March/April1987 and "Pro-gram Trading and Individual StockReturns:Ingredients of the Trple-WitchingBrew,"Journalof Business63(1990), 165-92.5. A. Kling, "How the Stock MarketCan Learn to Live with Index Fu-tures and Options," FinancialAna-lysts Journal September/October1987.6 Stoll and Whaley, "ProgramTrad-ing and Expiration Day Effects,"op.cit7. H R Stoll and R Whaley, "IndexFutures,Program Trading andStock Market Procedures,"Journalof FuturesMarkets8 (1988), 391-412.8. H R. Stoll and R. Whaley, "Expira-tion-Day Effects:WhatHasChanged?"Financial AnalystsJour-nal January/February 1991.9. S. P. Feinstein and W N Goetz-mann, "TheEffect of the 'TripleWitchingHour' on StockMarketVolatility,"Economic Review, Sep-tember/October1988.10. Stoll and Whaley, "Program Trad-ing and Individual StockReturns,"op. cit11. A F Herbstand E D. Maberly,"Stock ndex Futures, ExpirationDay Volatility,and the 'Special'Fri-day Opening:A Note,"Journal ofFutures Markets10 (1990), 323-25.

12. C Torres,"BigBoard Seeks Curbon Option,Futures Volatility,"WallStreet Journal, September21, 1990.13. The data were obtainedfrom theChicago MercantileExchange withthepermission of the Standard &Poor's Corporation.14 R. W Masulis, "TheEffectsof Capi-tal Structure Changes on SecurityPrices:A Study of Exchange Offers,"Journalof Financial EconomicsJune 1980.15. Thisdoes not mean that individualstocks cannot be affected by the ex-piration of derivatives,but only thatthe market as a whole is not af-fected.16 Even so, other days of the weekwere usedfor comparison purposes;no change in the end results wasobserved.17. R L.Inman and W j Conover,Modern Business Statistics(NewYork: ohn Wiley&Sons, 1983).18. Note that

AREi=>l ri,t/ 15 and

ARE= AREi/ 9.t=1

19. The F-ratio is SI/S, when Se > S,and SJIe when Sc > S,20. See Stoll and Whaley,"ProgramTrading and Expiration Day Ef-fects," "IndexFutures,ProgramTrading and Stock Market Proce-dures" and "ProgramTrading andIndividual Stock Returns,"op. cit21. j j Merrick, r., "VolumeDetermi-nation in Stock and Stock IndexFutures Markets:An Analysis of Ar-bitrage and VolatilityEfects,"Jour-nal of Futures Markets 7 (1987),483-96, and S Beckers, "Variancesof SecurityPrice Returns Based onHigh, Low and Closing Prices,"Joumal of Business 56 (1986), 97-112.

22. Merrick,"VolumeDetermination,"op. cit23. Stoll and Whaley, "ProgramTrad-ing and Expiration Day Effects,"op. cit

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